Import data into AWS RDS sql server through SQL Server management studio
There are stored procedures that you can do on Rds

EXEC rds_backup_database 'DBName','.bak file path','','0'

EXEC rds_restore_database 'DBName','.bak file path',''


File path use S3.

Just to add more context for the op.

The RDS instance doesn't give you access to the underlying file system like an ec2 would, hence you have to use s3 buckets.

See here for full details:-
http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/SQLServer.Procedural.Importing.html