I started working on my OPT starting January 2nd 2011. Starting 2011 was my 6th year on my F1 visa. In January 2012 I converted from F1 to H1 status.

Now I am wondering if there is any way of claiming FICA exempt for 2011 since I was working on OPT (full-time). I was also working for a University if that helps?

No, there is no way to avoid the FICA taxes for 2011 or 2012.

You became liable for FICA (Social Security and Medicare) taxes under the five-year rule on 1 January 2011. You CAN POSSIBLY extend the exemption if you can prove the "cloer connection" to your home country, but that argument went out the window when you applied for the H-1B visa.

Now, under a separate law that has NOTHING to do with your visa status, college students are exempt from FICA taxes if they are working part-time on university grounds.

But I doubt that your OPT is with the university, so MAKE SURE your OPT employer knows that you ARE liable for FICA taxes. You have that legal obligation to notify him, preferably in writing. Email is good for this.

You are resident for 2011. So in 2012 your days on F1 are not exempt from residency.