Yes, DRAWER is a Scrabble word!

Letter values in Scrabble US: D 2, R 1, A 1, W 4, E 1, R 1.

Is it a valid word?

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

a boxlike container in a piece of furniture; made so as to slide in and out
the person who writes a check or draft instructing the drawee to pay someone else
an artist skilled at drawing