Actually, Shakespeare never used this specific phrase. If he had, the gramtically correct way to say it would be "I bite my thumb at thee!".
Why should you care about Thumb Biting in William Shakespeare's Romeo and Juliet? We have the answers here, in a quick and easy way.
Here is an answer from googolfarmer.info: You can see a few depictions of thumb- biting in this compilation, involving spitting for the most part.