They recruit for QA all year but primarily January. You are much more likely to get a job if you have previous experience in QA or a game related degree. Try to find a recruiter and message them, listing your credentials and see if you can get an interview. That's how my husband got a job :) good luck!
I believe if you sign up for EA Access, they will occasionally send out emails requesting testers in various cities/areas. Not sure about careers, however.
Thanks! Your answer is awaiting moderation.