diff --git a/moto/rds/models.py b/moto/rds/models.py
--- a/moto/rds/models.py
+++ b/moto/rds/models.py
@@ -220,6 +220,10 @@ def is_multi_az(self) -> bool:
             or self.replication_source_identifier is not None
         )
 
+    @property
+    def arn(self) -> str:
+        return self.db_cluster_arn
+
     @property
     def db_cluster_arn(self) -> str:
         return f"arn:aws:rds:{self.region_name}:{self.account_id}:cluster:{self.db_cluster_identifier}"
@@ -461,6 +465,10 @@ def __init__(
             datetime.datetime.utcnow()
         )
 
+    @property
+    def arn(self) -> str:
+        return self.snapshot_arn
+
     @property
     def snapshot_arn(self) -> str:
         return f"arn:aws:rds:{self.cluster.region_name}:{self.cluster.account_id}:cluster-snapshot:{self.snapshot_id}"
@@ -645,6 +653,10 @@ def __init__(self, **kwargs: Any):
             kwargs.get("enable_cloudwatch_logs_exports") or []
         )
 
+    @property
+    def arn(self) -> str:
+        return self.db_instance_arn
+
     @property
     def db_instance_arn(self) -> str:
         return f"arn:aws:rds:{self.region_name}:{self.account_id}:db:{self.db_instance_identifier}"
@@ -1091,6 +1103,10 @@ def __init__(
             datetime.datetime.utcnow()
         )
 
+    @property
+    def arn(self) -> str:
+        return self.snapshot_arn
+
     @property
     def snapshot_arn(self) -> str:
         return f"arn:aws:rds:{self.database.region_name}:{self.database.account_id}:snapshot:{self.snapshot_id}"
diff --git a/moto/resourcegroupstaggingapi/models.py b/moto/resourcegroupstaggingapi/models.py
--- a/moto/resourcegroupstaggingapi/models.py
+++ b/moto/resourcegroupstaggingapi/models.py
@@ -2,6 +2,7 @@
 from moto.core import BaseBackend, BackendDict
 from moto.core.exceptions import RESTError
 from moto.moto_api._internal import mock_random
+from moto.utilities.tagging_service import TaggingService
 
 from moto.s3.models import s3_backends, S3Backend
 from moto.ec2 import ec2_backends
@@ -370,71 +371,32 @@ def format_tag_keys(
 
                 yield {"ResourceARN": f"{kms_key.arn}", "Tags": tags}
 
-        # RDS Cluster
-        if (
-            not resource_type_filters
-            or "rds" in resource_type_filters
-            or "rds:cluster" in resource_type_filters
-        ):
-            for rds_cluster in self.rds_backend.clusters.values():
-                tags = rds_cluster.get_tags()
-                if not tags or not tag_filter(tags):
-                    continue
-                yield {
-                    "ResourceARN": rds_cluster.db_cluster_arn,
-                    "Tags": tags,
-                }
-
-        # RDS Instance
-        if (
-            not resource_type_filters
-            or "rds" in resource_type_filters
-            or "rds:db" in resource_type_filters
-        ):
-            for database in self.rds_backend.databases.values():
-                tags = database.get_tags()
-                if not tags or not tag_filter(tags):
-                    continue
-                yield {
-                    "ResourceARN": database.db_instance_arn,
-                    "Tags": tags,
-                }
+        # RDS resources
+        resource_map: Dict[str, Dict[str, Any]] = {
+            "rds:cluster": self.rds_backend.clusters,
+            "rds:db": self.rds_backend.databases,
+            "rds:snapshot": self.rds_backend.database_snapshots,
+            "rds:cluster-snapshot": self.rds_backend.cluster_snapshots,
+        }
+        for resource_type, resource_source in resource_map.items():
+            if (
+                not resource_type_filters
+                or "rds" in resource_type_filters
+                or resource_type in resource_type_filters
+            ):
+                for resource in resource_source.values():
+                    tags = resource.get_tags()
+                    if not tags or not tag_filter(tags):
+                        continue
+                    yield {
+                        "ResourceARN": resource.arn,
+                        "Tags": tags,
+                    }
 
         # RDS Reserved Database Instance
         # RDS Option Group
         # RDS Parameter Group
         # RDS Security Group
-
-        # RDS Snapshot
-        if (
-            not resource_type_filters
-            or "rds" in resource_type_filters
-            or "rds:snapshot" in resource_type_filters
-        ):
-            for snapshot in self.rds_backend.database_snapshots.values():
-                tags = snapshot.get_tags()
-                if not tags or not tag_filter(tags):
-                    continue
-                yield {
-                    "ResourceARN": snapshot.snapshot_arn,
-                    "Tags": tags,
-                }
-
-        # RDS Cluster Snapshot
-        if (
-            not resource_type_filters
-            or "rds" in resource_type_filters
-            or "rds:cluster-snapshot" in resource_type_filters
-        ):
-            for snapshot in self.rds_backend.cluster_snapshots.values():
-                tags = snapshot.get_tags()
-                if not tags or not tag_filter(tags):
-                    continue
-                yield {
-                    "ResourceARN": snapshot.snapshot_arn,
-                    "Tags": tags,
-                }
-
         # RDS Subnet Group
         # RDS Event Subscription
 
@@ -767,14 +729,27 @@ def get_tag_values(
 
         return new_token, result
 
-    # These methods will be called from responses.py.
-    # They should call a tag function inside of the moto module
-    # that governs the resource, that way if the target module
-    # changes how tags are delt with theres less to change
+    def tag_resources(
+        self, resource_arns: List[str], tags: Dict[str, str]
+    ) -> Dict[str, Dict[str, Any]]:
+        """
+        Only RDS resources are currently supported
+        """
+        missing_resources = []
+        missing_error: Dict[str, Any] = {
+            "StatusCode": 404,
+            "ErrorCode": "InternalServiceException",
+            "ErrorMessage": "Service not yet supported",
+        }
+        for arn in resource_arns:
+            if arn.startswith("arn:aws:rds:"):
+                self.rds_backend.add_tags_to_resource(
+                    arn, TaggingService.convert_dict_to_tags_input(tags)
+                )
+            else:
+                missing_resources.append(arn)
+        return {arn: missing_error for arn in missing_resources}
 
-    # def tag_resources(self, resource_arn_list, tags):
-    #     return failed_resources_map
-    #
     # def untag_resources(self, resource_arn_list, tag_keys):
     #     return failed_resources_map
 
diff --git a/moto/resourcegroupstaggingapi/responses.py b/moto/resourcegroupstaggingapi/responses.py
--- a/moto/resourcegroupstaggingapi/responses.py
+++ b/moto/resourcegroupstaggingapi/responses.py
@@ -58,21 +58,15 @@ def get_tag_values(self) -> str:
 
         return json.dumps(response)
 
-    # These methods are all thats left to be implemented
-    # the response is already set up, all thats needed is
-    # the respective model function to be implemented.
-    #
-    # def tag_resources(self):
-    #     resource_arn_list = self._get_list_prefix("ResourceARNList.member")
-    #     tags = self._get_param("Tags")
-    #     failed_resources_map = self.backend.tag_resources(
-    #         resource_arn_list=resource_arn_list,
-    #         tags=tags,
-    #     )
-    #
-    #     # failed_resources_map should be {'resource': {'ErrorCode': str, 'ErrorMessage': str, 'StatusCode': int}}
-    #     return json.dumps({'FailedResourcesMap': failed_resources_map})
-    #
+    def tag_resources(self) -> str:
+        resource_arns = self._get_param("ResourceARNList")
+        tags = self._get_param("Tags")
+        failed_resources = self.backend.tag_resources(
+            resource_arns=resource_arns, tags=tags
+        )
+
+        return json.dumps({"FailedResourcesMap": failed_resources})
+
     # def untag_resources(self):
     #     resource_arn_list = self._get_list_prefix("ResourceARNList.member")
     #     tag_keys = self._get_list_prefix("TagKeys.member")

Hi @klauern, welcome to Moto!

Support for the `resourcegroupstaggingapi` is a bit trickier, because it supports tagging all the services. There is no centralized tagging mechanism in Moto (yet), so this means we will have to implement this feature for every service separately. I imagine that we'll only implement support for a few services/resources at the time, based on what is required. 

Is there a specific service-resource(s) that you want to tag using this API?
I was using [CloudCustodian](cloudcustodian.io) to write some policies around tagging/archival tasks around RDS DB cluster snapshot ages, and it apparently uses that API to get the tagging done.  It took a bit of fiddling to figure that out, but when the test started erroring on `tag_resources`, I found it wasn't using the RDS mock in the test for that action.  I'm not sure what other places CC uses that API, but it does seem like a fallback mechanism/simplification for tagging suport across different resources with an ARN
diff --git a/tests/test_resourcegroupstaggingapi/test_resourcegroupstagging_rds.py b/tests/test_resourcegroupstaggingapi/test_resourcegroupstagging_rds.py
new file mode 100644
--- /dev/null
+++ b/tests/test_resourcegroupstaggingapi/test_resourcegroupstagging_rds.py
@@ -0,0 +1,71 @@
+import boto3
+import unittest
+
+from moto import mock_rds
+from moto import mock_resourcegroupstaggingapi
+
+
+@mock_rds
+@mock_resourcegroupstaggingapi
+class TestRdsTagging(unittest.TestCase):
+    def setUp(self) -> None:
+        self.rds = boto3.client("rds", region_name="us-west-2")
+        self.rtapi = boto3.client("resourcegroupstaggingapi", region_name="us-west-2")
+        self.resources_tagged = []
+        self.resources_untagged = []
+        for i in range(3):
+            database = self.rds.create_db_instance(
+                DBInstanceIdentifier=f"db-instance-{i}",
+                Engine="postgres",
+                DBInstanceClass="db.m1.small",
+                CopyTagsToSnapshot=bool(i),
+                Tags=[{"Key": "test", "Value": f"value-{i}"}] if i else [],
+            ).get("DBInstance")
+            snapshot = self.rds.create_db_snapshot(
+                DBInstanceIdentifier=database["DBInstanceIdentifier"],
+                DBSnapshotIdentifier=f"snapshot-{i}",
+            ).get("DBSnapshot")
+            group = self.resources_tagged if i else self.resources_untagged
+            group.append(database["DBInstanceArn"])
+            group.append(snapshot["DBSnapshotArn"])
+
+    def test_get_resources_rds(self):
+        def assert_response(response, expected_count, resource_type=None):
+            results = response.get("ResourceTagMappingList", [])
+            assert len(results) == expected_count
+            for item in results:
+                arn = item["ResourceARN"]
+                assert arn in self.resources_tagged
+                assert arn not in self.resources_untagged
+                if resource_type:
+                    assert f":{resource_type}:" in arn
+
+        resp = self.rtapi.get_resources(ResourceTypeFilters=["rds"])
+        assert_response(resp, 4)
+        resp = self.rtapi.get_resources(ResourceTypeFilters=["rds:db"])
+        assert_response(resp, 2, resource_type="db")
+        resp = self.rtapi.get_resources(ResourceTypeFilters=["rds:snapshot"])
+        assert_response(resp, 2, resource_type="snapshot")
+        resp = self.rtapi.get_resources(
+            TagFilters=[{"Key": "test", "Values": ["value-1"]}]
+        )
+        assert_response(resp, 2)
+
+    def test_tag_resources_rds(self):
+        # WHEN
+        # we tag resources
+        self.rtapi.tag_resources(
+            ResourceARNList=self.resources_tagged,
+            Tags={"key1": "value1", "key2": "value2"},
+        )
+
+        # THEN
+        # we can retrieve the tags using the RDS API
+        def get_tags(arn):
+            return self.rds.list_tags_for_resource(ResourceName=arn)["TagList"]
+
+        for arn in self.resources_tagged:
+            assert {"Key": "key1", "Value": "value1"} in get_tags(arn)
+            assert {"Key": "key2", "Value": "value2"} in get_tags(arn)
+        for arn in self.resources_untagged:
+            assert get_tags(arn) == []
diff --git a/tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py b/tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py
--- a/tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py
+++ b/tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py
@@ -6,7 +6,6 @@
 from moto import mock_ec2
 from moto import mock_elbv2
 from moto import mock_kms
-from moto import mock_rds
 from moto import mock_resourcegroupstaggingapi
 from moto import mock_s3
 from moto import mock_lambda
@@ -223,7 +222,6 @@ def test_get_resources_ecs():
     assert task_two not in resp["ResourceTagMappingList"][0]["ResourceARN"]
 
 
-@mock_rds
 @mock_ec2
 @mock_resourcegroupstaggingapi
 def test_get_resources_ec2():
@@ -588,49 +586,6 @@ def test_multiple_tag_filters():
     assert instance_2_id not in results[0]["ResourceARN"]
 
 
-@mock_rds
-@mock_resourcegroupstaggingapi
-def test_get_resources_rds():
-    client = boto3.client("rds", region_name="us-west-2")
-    resources_tagged = []
-    resources_untagged = []
-    for i in range(3):
-        database = client.create_db_instance(
-            DBInstanceIdentifier=f"db-instance-{i}",
-            Engine="postgres",
-            DBInstanceClass="db.m1.small",
-            CopyTagsToSnapshot=bool(i),
-            Tags=[{"Key": "test", "Value": f"value-{i}"}] if i else [],
-        ).get("DBInstance")
-        snapshot = client.create_db_snapshot(
-            DBInstanceIdentifier=database["DBInstanceIdentifier"],
-            DBSnapshotIdentifier=f"snapshot-{i}",
-        ).get("DBSnapshot")
-        group = resources_tagged if i else resources_untagged
-        group.append(database["DBInstanceArn"])
-        group.append(snapshot["DBSnapshotArn"])
-
-    def assert_response(response, expected_count, resource_type=None):
-        results = response.get("ResourceTagMappingList", [])
-        assert len(results) == expected_count
-        for item in results:
-            arn = item["ResourceARN"]
-            assert arn in resources_tagged
-            assert arn not in resources_untagged
-            if resource_type:
-                assert f":{resource_type}:" in arn
-
-    rtapi = boto3.client("resourcegroupstaggingapi", region_name="us-west-2")
-    resp = rtapi.get_resources(ResourceTypeFilters=["rds"])
-    assert_response(resp, 4)
-    resp = rtapi.get_resources(ResourceTypeFilters=["rds:db"])
-    assert_response(resp, 2, resource_type="db")
-    resp = rtapi.get_resources(ResourceTypeFilters=["rds:snapshot"])
-    assert_response(resp, 2, resource_type="snapshot")
-    resp = rtapi.get_resources(TagFilters=[{"Key": "test", "Values": ["value-1"]}])
-    assert_response(resp, 2)
-
-
 @mock_lambda
 @mock_resourcegroupstaggingapi
 @mock_iam
@@ -717,3 +672,17 @@ def assert_response(response, expected_arns):
 
     resp = rtapi.get_resources(TagFilters=[{"Key": "Shape", "Values": ["rectangle"]}])
     assert_response(resp, [rectangle_arn])
+
+
+@mock_resourcegroupstaggingapi
+def test_tag_resources_for_unknown_service():
+    rtapi = boto3.client("resourcegroupstaggingapi", region_name="us-west-2")
+    missing_resources = rtapi.tag_resources(
+        ResourceARNList=["arn:aws:service_x"], Tags={"key1": "k", "key2": "v"}
+    )["FailedResourcesMap"]
+
+    assert "arn:aws:service_x" in missing_resources
+    assert (
+        missing_resources["arn:aws:service_x"]["ErrorCode"]
+        == "InternalServiceException"
+    )

Add `tag_resources` support to resourcegroupstaggingapi
This is in addition to https://github.com/getmoto/moto/issues/6669 which was for the `log` API endpoint.  This also applies to the `resourcegroupstaggingapi` endpoint.


tests/test_resourcegroupstaggingapi/test_resourcegroupstagging_rds.py::TestRdsTagging::test_tag_resources_rds tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_tag_resources_for_unknown_service
tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_resources_s3 tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_many_resources tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_resources_lambda tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_tag_values_ec2 tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_resources_ecs tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_resources_cloudformation tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_resources_ec2 tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_multiple_tag_filters tests/test_resourcegroupstaggingapi/test_resourcegroupstagging_rds.py::TestRdsTagging::test_get_resources_rds tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_tag_keys_ec2 tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_resources_target_group tests/test_resourcegroupstaggingapi/test_resourcegroupstaggingapi.py::test_get_resources_ec2_vpc