I am a 20 year old college student. My mom got married in 2016 and will file a joint return with her husband this year. Can they still claim me as a dependent?

Yes, if you are a full time student living with them when not in school and no one else can claim you.

Thanks! I had minimal income from a job at school but am required to file I believe. I am not eligible for the college credit because I am being claimed as a dependent by my mom. Does this make sense?

Yes. You cannot claim education credit because you are a dependent.  Mom will claim it.