Yes, SHOOTER is a Scrabble word!

Letter values in Scrabble US: S 1, H 4, O 1, O 1, T 1, E 1, R 1.

Is it a valid word?

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

a large marble used for shooting in the game of marbles
a person who shoots (usually with respect to their ability to shoot)
a gambler who throws dice in the game of craps
(sports) a player who drives or kicks a ball at the goal (or a basketball player who shoots at the basket)
a professional killer who uses a gun

Also: crap-shooter, hired gun, gun for hire, hit man.