Yes, SECRET is a Scrabble word!

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

Is it a valid word?

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

something that should remain hidden from others (especially information that is not to be passed on)
information known only to a special group
something that baffles understanding and cannot be explained

not open or public; kept private or not revealed
conducted with or marked by hidden aims or methods
not openly made known
communicated covertly
not expressed
designed to elude detection
hidden from general view or use
(of information) given in confidence or in secret
indulging only covertly
having an import not apparent to the senses nor obvious to the intelligence; beyond ordinary understanding
the next to highest level of official classification for documents

Also: closed book, cloak-and-dagger, hole-and-corner, hugger-mugger, hush-hush.