A "Like" on Facebook is usually is a "Star" (or "add to favorites") on Twitter. For an overview of tweets that received stars, Favstar.fm seems to be the most common site. As long as it is about single tweets the star seems to be the established symbol of "I like".
When it comes to just linking to a related Twitter account, I guess there are multiple button-like images that Twitter provides for linking.
Like this one Follow Me - button http://twitter-badges.s3.amazonaws.com/follow_bird-b.png, which looks similar to your custom one.
I hope this is helpful, otherwise it seems I did not fully understand what you were looking for.