No, you cannot use rsync to transfer files to Amazon. It uses its own protocol for the service. But you can access their storage via third-party services, like www.s3rsync.com, then you'll be able to use rsync, and your data will be finally transfered to S3 storage.
Or you can use special utilities designed for S3 storage. There are: s3sync, s3command, s3cp, tarsnap (tarsnap is a third party service, like s3rsync).
Another rsync-like tool, duplicity, supports S3 storage as a backend as well as many other backup backends, including RackSpace Cloud Files (another cloud storage service, priced similarly to Amazon S3).
Backup to S3:
duplicity /home/me s3+http://bucketname/prefix
or to Rackspace's Cloud Files:
duplicity /home/me cf+http://container_name