Yes, QUANTIFIER is a Scrabble word!

Letter values in Scrabble US: Q 10, U 1, A 1, N 1, T 1, I 1, F 4, I 1, E 1, R 1.

Is it a valid word?

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

(logic) a word (such as `some' or `all' or `no') that binds the variables in a logical proposition
(grammar) a word that expresses a quantity (as `fifteen' or `many')

Also: logical quantifier.