Yes, PROCESSOR is a Scrabble word!

Letter values in Scrabble US: P 3, R 1, O 1, C 3, E 1, S 1, S 1, O 1, R 1.

Is it a valid word?

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

a business engaged in processing agricultural products and preparing them for market
someone who processes things (foods or photographs or applicants etc.)
(computer science) the part of a computer (a microprocessor chip) that does most of the data processing

Also: central processing unit, c.p.u., central processor.

Not playable in Scrabble US: CPU.