You can use Git on your own without anyone else being affected. It doesn't require a server to add benefit. Learn to work with it and then introduce your coworkers later.
I've done exactly this ~4 years ago when I briefly worked at a place that used Subversion, after an acquisition. I wanted to be able to dick around in my own branches, with proper diffing and tracking and all, without updating the server, which appeared to be impossible (more or less). There was a git-to-svn I could use but considering how easy it was to screw up other people's state in Subversion, it made me nervous. So I just worked in my own, local git then copied the files to SVN when ready to commit something worth sharing.
Sublime-merge (the Gui git client from the sublime text people) is available in a portable version, and so can be run as a .exe from the filesystem, or a mountable drive. Comes with its own git binary.
The GUI is stunningly beautiful and functional, and there are more than enough keyboard shortcuts to keep things snappy once you're in the flow. I used to live and die by the terminal, now I am in love with sublime merge.
I used the portable version for a job where I didn't have install rights to the corporate laptop, and it preserved my workflow and kept me sane during my dev work. The portable version can run a little slow, but it's a pretty good solution.
I'm in a similar situation and the entire git for windows setup (including git bash that works beautifully with things like Windows network drives!) can be used without ever needing admin privileges. So I not only have git but also vim and perl and the whole *nix kit I was so sorely missing.
Some truly locked down environments may not allow it but if the poster has other open source tools like R they can probably run .exe files.
