Yes, WRONGER is a Scrabble word!

Letter values in Scrabble US: W 4, R 1, O 1, N 1, G 2, E 1, R 1.

Is it a valid word?

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

not correct; not in conformity with fact or truth
contrary to conscience or morality or law
not appropriate for a purpose or occasion
not functioning properly
based on or acting or judging in error
not in accord with established usage or procedure
used of the side of cloth or clothing intended to face inward
badly timed
characterized by errors; not agreeing with a model or not following established rules; the wrong side of the road"

Also: ill-timed.