Beginner question: automate uploading theme to server

Hi all,

This is more like a general setup question.

At the moment, I'm using a local WordPress install with Mamp-Pro to test my WordPress themes. All working fine but when I want to test the theme on my online test-server, I need to do the following:

1. login to the testserver
2. change theme
3. delete the previous version of the theme
4. zip the new version of the theme
5. upload the new version of the theme
6. activate the new version of the theme

I bought Git-Kraken for version control in the hope that this would make it possible to simply 'git-push' the new version, but I'm not sure if it can be done, or how it needs to be setup.

Can anyone advise please?

Thank you very much!

kind regards,