A new post (or a custom post type is that option is selected) will be created every time a release is made on GitHub. You can display the release post with your other posts or use the shortcode to generate changelogs or links to the latest release.

Release listener for GitHub

Listens to a GitHub webhook and creates a new post every time a release is made.

rubengarzajr

GitSync adds a new option to the admin dashboard that allows you to add a Theme from Github. 
When properly configured, you can then pick a release to be downloaded to your instance of WordPress.
Just enter the URI of the repo and your personal token and then click Add Theme. 
You’ll then see the repo list below in the Installed Themes area.
Just choose a release and click on “Sync to the release.”

GitSync

Download and sync themes from github.com or private github using release tags.

Release listener for GitHub vs GitSync