Yes, PROMPTER is a Scrabble word!

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

Is it a valid word?

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

someone who assists a performer by providing the next words of a forgotten speech
a device that displays words for people to read

Also: theater prompter.

Not playable in Scrabble US: AUTOCUE.