Git Push to Amazon S3 for Deploying Assets?
You can use s3cmd --sync LOCAL s3://BUCKET/PREFIX to accomplish this. It is best if each asset has a version number in its name. Otherwise you can have weird issues such as the browser caching version 1 of the CSS and using version 2 of the JavaScript, causing undefined behavior.
How about setting up an EC2 image, mounting the s3 image on there and setting up a bare git repository to push to on said S3 image?
Tools recommend by other answers are out of date.
This one is up to date: https://github.com/schickling/git-s3