I recently created a fanpage to my site and added a +1 button to it.
I would like to connect my +1 button on my website to the +1 button on my fanpage. I mean - when you +1 in my website and the link you +1 is of the website, it will also add +1 in my google's fanpage.
Is it possible to do it?
You are looking for Google+ Direct Connect. It was recently launched and last I heard the merging of the +1 counts may take some time.