Yes, VARSITY is a Scrabble word!

Letter values in Scrabble US: V 4, A 1, R 1, S 1, I 1, T 1, Y 4.

Is it a valid word?

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

a British abbreviation of `university'; usually refers to Oxford University or Cambridge University
a team representing a college or university

Also: first team.