Yes, REM is a Scrabble word!

Letter values in Scrabble US: R 1, E 1, M 3.

Is it a valid word?

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

a recurring sleep state during which dreaming occurs; a state of rapidly shifting eye movements during sleep
(Roentgen Equivalent Man) the dosage of ionizing radiation that will cause the same amount of injury to human tissue as 1 roentgen of X-rays

Also: paradoxical sleep, rapid eye movement sleep, rem sleep, rapid eye movement.