CC-Update

This plugin allows you to automatically send changes to your GIT repository, immediately after any update is made on your site.

If you store the source code of your website in the GIT repository, you can use this plugin to automatically send changes in the website’s code to the repository after each update.
The plugin checks for updates (core, plugin, theme, translation) in a selected time interval, creates a new commit, and makes a push to the GIT repository.
The plugin supports automatic WordPress updates. After each action the plugin saves the status to logs which are available through wp-admin and also are sent by email to defined recipients.