Yes, MAJORS is a Scrabble word!

Letter values in Scrabble US: M 3, A 1, J 8, O 1, R 1, S 1.

Is it a valid word?

MAJORS is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

the most important league in any sport (especially baseball)
a commissioned military officer in the United States Army or Air Force or Marines; below lieutenant colonel and above captain
British statesman who was prime minister from 1990 until 1997 (born in 1943)
a university student who is studying a particular field as the principal subject
the principal field of study of a student at a university

Also: major league, big league, john major, john r. major, john roy major.