Yes, BESMIRCH is a Scrabble word!

Letter values in Scrabble US: B 3, E 1, S 1, M 3, I 1, R 1, C 3, H 4.

Is it a valid word?

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

charge falsely or with malicious intent; attack the good name and reputation of someone
smear so as to make dirty or stained