I know Google Plus only provides a read only API hence creating auto posting apps for Google Plus is yet not possible but PHP solves this problem. Dmitry Sandalov’s standalone PHP script makes auto publishing to Google+ possible.
You may use this feature on your WordPress site by install and activating his WPGPlus plugin and make your post automatically getting posted to Google+ profile after getting published on WordPress blog. After activation navigate to Settings->WPGPlus and enter your GooglePlus username and password, click save button.
He is still working on cleaning up the output, getting G+ to recognize links and show images, and compatible to posts to Google Plus Pages etc.