Is there a website that shows a list of followers who follow back? (Twitter)?

[Rodrigo Duran]

[Patricia]

Don't know about such a thing but following random people around seems like a huge waste of time to me.
Why don't you try an active social media exchange method? Like http://youpluslike.com/ for example.
You can basically exchange followers clean and easy with other people. Same as following people "who follow back" only this way its guaranteed since the system is automatic and doesn't allow people NOT to follow.