Yes, MARRIAGE is a Scrabble word!

Letter values in Scrabble US: M 3, A 1, R 1, R 1, I 1, A 1, G 2, E 1.

Is it a valid word?

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

the state of being a married couple voluntarily joined for life (or until divorce)
two people who are married to each other
the act of marrying; the nuptial ceremony
a close and intimate union

Also: spousal relationship, married couple, man and wife, marriage ceremony.