I entered the country in August 2008 on an F1 visa for my undergraduate studies. I worked part time for 6 months before graduating in September 2011. I have been working full time on OPT and Stem OPT since October 2011. I had FICA taxes withheld from my paycheck in both 2011 and 2012.
My understanding is :
I am exempt from FICA taxes for my first 5 calendar years in the country. My 5th calendar year ends in August 2013. That entails that I am exempt from FICA taxes till December 31st 2012.
Am I correct?
Also, if my employer is not acknowledging this, how can I apply for a refund? I have filed my 1040-NR-EZ for both 2011 and 2012.
Thank you for the help!

Actually, 2012 was your last exempt year. You became liable for FICA (Social Security and Medicare) taxes on 1 Jan 2013.

To collect improperly-withheld FICA taxes direct from the IRS, you must submit Form 843 and 8316 along with multiple support documents to the IRS center in Austin, TX.

Also, you will file as a resident (Form 1040) for 2013.

If you need professional help with this process, email me at the address in my profile.