Heroku is a free cloud hosting service that lets you scale and things.

Using MySQL with Rails applications on Heroku

This is actually very difficult because by default Heroku overwrites your database.yml, you need to follow the instructions for Configuring your Ruby application to use ClearDB:

heroku config | grep CLEARDB_DATABASE_URL
heroku config:set DATABASE_URL='mysql://example:example@us-cdbr-east.cleardb.com/heroku_db?reconnect=true'