Can I get denied if I was arrested in 2011 and charged with assault in a 3rd degree?

You may be denied or your decision delayed. You need to prove to the satisfaction of USCIS that you have good moral character for the required period of 3 or 5 years depending upon whether you became a permanent resident through marriage. There may be other complications, so I recommend an appointment with a competent and experienced immigration attorney. Good luck.