A webapp called 2FB (find it at 2FB.me ) let's other people share your Tweets to their own Facebook page. Think of this as having Facebook LIKE buttons on your Tweets.
It's a new concept that some users have a hard time understanding at first. But for those that get it, it's powerful and proving viral.
Here is a comprehensive tutorial
(1) Enter your Twitter name in the box
(2) Click [OK] or wait 5 seconds for the link code
(3) Click [Copy and Paste] and enter your Tweet in the window, or paste your link code to a tweet
> Tweet and your done! (You can freely include links, hashes, symbols, etc. in your tweet)
If you use Twitter share buttons regularly. There is a chrome extension that makes it even more simple. It puts LIKE links on your tweets automatically.