github only hosts the source code and no compiled versions. you clone the source repository using git and compile it yourself. there is a feed for commits https://github.com/bitcoin/bitcoin/commits/v0.3.24rc3.atom but not for tags, which would probably be the best way to determine a "stable" version.

precompiled binaries are hosted on sourceforge and there appears to be an rss feed: http://sourceforge.net/api/file/index/project-id/244765/mtime/desc/limit/20/rss