Yes, ANALOGY is a Scrabble word!

Letter values in Scrabble US: A 1, N 1, A 1, L 1, O 1, G 2, Y 4.

Is it a valid word?

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

an inference that if things agree in some respects they probably agree in others
drawing a comparison in order to show a similarity in some respect
the religious belief that between creature and creator no similarity can be found so great but that the dissimilarity is always greater; any analogy between God and humans will always be inadequate

Also: doctrine of analogy.