...
WPEngine provides a “no CI” method of deploying and managing WordPress instances via Git. By integrating WPEngine as a remote, you can leverage their Git hooks to update code.
Setting Up
git remote add wpe-dev git@git.wpengine.com:<remote-environment>/<project>.git will add the remote to your cloned Git repo. Run git remote -v to ensure that the remote is properly registered.
Usage
So long as the project has been set up properly, you should then be able to push to a given remote server git push <remote> <branch>