You can snapshot your RDS database and restore it as an Aurora DB. Only caveat is it has to be MySQL 5.6.
http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/Aurora...
http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/Aurora...
DMS gets closer than the above link, I think, since it will handle replication onto the target database for you. But, for two fully compatible database engines, it seems like you should be able to make the switch without having to fuss with replication configuration or spinning up a new instance at all.