Create Tagged Git Archives from Existing Tarballs
Yes and no. Git doesn't track revisions internally the way you think it does, but you can certainly use tags to create archives that match your current tarballs. For example:
git init
# Unpack version 1.0
tar xvfz /tmp/foo.tar.gz
git add .
git commit -m 'Add version 1.0'
git tag v1.0
# Remove files with GNU find before unpacking next archive.
find . -name .git -prune -o -exec rm {} +
You could then do the same, in order, for your other archived versions. Skip the find command when you're done adding versions. Then, when you push your tags to GitHub, each tag becomes available as a Git archive using the name of the tags you've created.