set :scm, :git # of course
set :deploy_via, :export
set :project, [insert-your-repo-subdir-here]
Which will cause capistrano to execute something along the lines of
git archive --format=tar --remote=[your-repo-path] \
to deploy your application, cool huh? The catch, well, not all repositories (notably github) support the archive command via the git protocol, but if you're hosting your own repository or connecting by ssh, this will work just fine.