Yes, COMPLAINT is a Scrabble word!

Letter values in Scrabble US: C 3, O 1, M 3, P 3, L 1, A 1, I 1, N 1, T 1.

Is it a valid word?

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

an often persistent bodily disorder or disease; a cause for complaining
(formerly) a loud cry (or repeated cries) of pain or rage or sorrow
an expression of grievance or resentment
(civil law) the first pleading of the plaintiff setting out the facts on which the claim for relief is based
(criminal law) a pleading describing some wrong or offense