Did you know that, Google offering shorten URL such as bit.ly services and other shorten URL services, using WP Goo.gl you can integrated your WordPress site and using Goo.gl shorten URL.
My we recommended this plugin? This is what WP Goo.gl developer has said
WP Goo.gl URL shortener plugin for wordpress allows you to shorten your wordpress URLs using Goo.gl.
This plugin will work with and with out Google authentication.