Is there a way to find the transaction count on a sql table?
You want to use the sys.dm_db_index_operational_stats DMF.

SELECT *
FROM sys.dm_db_index_operational_stats(DB_ID(), OBJECT_ID(N'schema.table'), NULL, NULL);


There is a lot of very interesting and useful info in that DMF, but with respect to this particular question, the following columns should have what you are looking for:


  leaf_insert_count -- bigint -- Cumulative count of leaf-level inserts.  
  
  leaf_delete_count -- bigint -- Cumulative count of leaf-level deletes. leaf_delete_count is only incremented for deleted records that are not marked as ghost first. For deleted records that are ghosted first, leaf_ghost_count is incremented instead.  
  
  leaf_update_count -- bigint -- Cumulative count of leaf-level updates.


It won't show history, so take a sample once per day. And like all DMVs and DMFs, it probably gets recent upon service restart.