vmassuchetto

This is a plugin for managing website releases under production or development 
environments. Once the WordPress installation is in a Git tree, WP Deploy will 
detect its branches and put a switch menu in the admin bar.
Like this, you can just push your website to your remote and use the menu to 
deploy the changes without using Git hooks or prompting into another shell.
Another useful purpose is for the development process, where different 
implementations can be viewed and switched by customers, or a production branch 
can be testes in a staging environment.

WP Git Deploy

Deploy websites using Git and the admin bar.

PiotrPress

Clearcode

This plugin allows you to deploy your WordPress site source code from git repository using webhooks.
Automatically pull from a repository to a web server. You can configure which branch is triggering the pull action. 
After each deployment plugin saves the status to logs which are available through wp-admin and also are sent by email.
Supported git repository hosting services: 
* <a href="https://github.com/" rel="nofollow ugc">Github</a> 
* <a href="https://bitbucket.org/" rel="nofollow ugc">Bitbucket</a> 
* Stash

CC-Deploy

This plugin allows you to deploy your WordPress site source code from git repository using webhooks.

WP Git Deploy vs CC-Deploy