Yes, COUNTER is a Scrabble word!

Letter values in Scrabble US: C 3, O 1, U 1, N 1, T 1, E 1, R 1.

Is it a valid word?

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

table consisting of a horizontal surface over which business is transacted
game equipment (as a piece of wood, plastic, or ivory) used for keeping a count or reserving a space in various card or board games
a calculator that keeps a record of the number of times something happens
a piece of furniture that stands at the side of a dining room; has shelves and drawers
a person who counts things
a quick reply to a question or remark (especially a witty or critical one)
(computer science) a register whose contents go through a regular series of states (usually states indicating consecutive integers)
a piece of leather forming the back of a shoe or boot
a return punch (especially by a boxer)

Also: heel counter.