You normally are eligible after five years of continuous presence in the U.S., after getting green card. The requirement drops to three years, under certain conditions, if you are married to U.S. citizen.
Whether you have "of arts" or "of science" degree makes no difference. The key is page 3 of your I-20. Next to your field of study is a code number, probably with a decimal point. That code is called the CIP code. If that code appears on the STEM list at the ICE website www.ice.gov the you are STEM-eligible for additional 17 months. Also, your employer must have e-Verify.