I am not entirely sure what you mean by "included in an application", as you could potentially deliver any library so long as the licensing allows. Are you referring to the fact that sqlite is small or that it is public domain?
Mercurial is a similarly lightweight piece of revision control software. If you are writing your application in python, which is likely since python now includes sqlite3, importing features directly from mercurial's source code should not be too difficult. Otherwise there's no shame in invoking commandline processes, though this may be clunkier. Mercurial is not public domain, but it is GPL'd.
Mercurial is also my personal favorite among modern revision control systems. It's leaps ahead of CVS and Subversion, and very similar to GIT although somewhat simpler to use.