Yes, FINISHER is a Scrabble word!

Letter values in Scrabble US: F 4, I 1, N 1, I 1, S 1, H 4, E 1, R 1.

Is it a valid word?

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

(baseball) a relief pitcher who can protect a lead in the last inning or two of the game
a racing driver who finishes a race
a painter who applies a finishing coat
a worker who performs the last step in a manufacturing process
a race car that finishes a race
an animal that wins in a contest of speed