If you are a member of Launchpad’s beta testers team, you can now try out Git-based recipes. These work very similarly to the Bazaar-based recipes that Launchpad has supported for a long time, with a few minor changes to handle differences in the underlying version control system: the main thing you’ll probably notice is that you almost always need to explicitly specify a branch name. The recipes documentation explains what to do; if you’re already familiar with how recipes work for Bazaar, then you should probably skip straight to the recipes guide to look over the differences for Git.
Please try this out and report any bugs you find. If all goes well, we’ll open this up to all users in a couple of weeks.
Update: as of 2016-03-15, this feature is enabled for all Launchpad users.