Yes, HANDSOME is a Scrabble word!

Letter values in Scrabble US: H 4, A 1, N 1, D 2, S 1, O 1, M 3, E 1.

Is it a valid word?

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

pleasing in appearance especially by reason of conformity to ideals of form and proportion
given or giving freely

Also: fine-looking, good-looking, better-looking, well-favored, well-favoured.