While plain rsync is fine for making backups periodically, rsync itself will not encrypt your data. Duplicity is a tool for that job. From their site:

Duplicity backs directories by producing encrypted tar-format volumes and uploading them to a remote or local file server. Because duplicity uses librsync, the incremental archives are space efficient and only record the parts of files that have changed since the last backup. Because duplicity uses GnuPG to encrypt and/or sign these archives, they will be safe from spying and/or modification by the server.

Read more at http://duplicity.nongnu.org/ Duplicity is available under GPL.