I am currently getting an MA degree in teaching ESL, do I also need to do a TEFL course to be able to teach abroad?

Hi,
Depending on the country you refer to as abroad, for Canada and The United Kingdom you'd need to achieve at least overall 7 bands out of 9 in IELTS, whereas, for Australia, New Zealand and The United States of America, you'd need overall 89+ score out of 120 for TOEFL.

Best Regards

Yes! You will mostly likely need a TEFL certificate to remain competitive in the ESL teaching market. Most Asian countries are hiring ESL teacher on a high demand. Having teaching experience isn't good enough to get yourself exposed in front of the big companies. A combination of advanced education and experience alongside certification will get you a stellar job as a ESL teacher.