Yes, CONTRADICTORY is a Scrabble word!

Letter values in Scrabble US: C 3, O 1, N 1, T 1, R 1, A 1, D 2, I 1, C 3, T 1, O 1, R 1, Y 4.

Is it a valid word?

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

two propositions are contradictories if both cannot be true (or both cannot be false) at the same time

of words or propositions so related that both cannot be true and both cannot be false
that confounds or contradicts or confuses
in disagreement
unable to be both true at the same time

Also: at odds, self-contradictory, mutually exclusive.