Steps to make a S3 hosted Git repository

$ export BUCKET=YOUR_BUCKET_NAME

# Only run these two commands once per bucket/repo
$ s3cmd mb s3://$BUCKET # aws s3 mb s3://$BUCKET
$ aws s3api put-bucket-acl --bucket $BUCKET --acl public-read

# Run These commands every time you wish to push to the S3 repo
$ git update-server-info
$ test -d .git && cd .git
$ s3cmd -P sync . s3://$BUCKET # aws s3 sync --acl public-read . s3://$BUCKET

# Run this once you want to clone from the S3 repo to another folder
$ git clone https://$BUCKET.s3.amazonaws.com

# Run this after cloning the repo to update from the latest changes pushed to S3
$ git pull

To be safer, you should probably use git bundle.