Yes, TROUSER is a Scrabble word!

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

Is it a valid word?

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

(usually in the plural) a garment extending from the waist to the knee or ankle, covering each leg separately
a garment (or part of a garment) designed for or relating to trousers