Yes, QUARTER is a Scrabble word!

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

Is it a valid word?

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

one of four equal parts
a district of a city having some distinguishing character
(football, professional basketball) one of four divisions into which some games are divided
a unit of time equal to 15 minutes or a quarter of an hour
one of four periods into which the school year is divided
a fourth part of a year; three months
one of the four major division of the compass
a quarter of a hundredweight (25 pounds)
a quarter of a hundredweight (28 pounds)
a United States or Canadian coin worth one fourth of a dollar
an unspecified person
the rear part of a ship
piece of leather that comprises the part of a shoe or boot covering the heel and joining the vamp
clemency or mercy shown to a defeated opponent

provide housing for (military personnel)
pull (a person) apart with four horses tied to his extremities, so as to execute him
divide into quarters
divide by four; divide into quarters

Also: one-fourth, one-quarter, fourth part, twenty-five percent, after part, draw and quarter.