Yes, ASSUME is a Scrabble word!

Letter values in Scrabble US: A 1, S 1, S 1, U 1, M 3, E 1.

Is it a valid word?

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

take to be the case or to be true; accept without verification or proof
take on titles, offices, duties, responsibilities
take on a certain form, attribute, or aspect
take on as one's own the expenses or debts of another person
occupy or take on
seize and take control without authority and possibly with force; take as one's right or possession
make a pretence of
take up someone's soul into heaven
put clothing on one's body

Also: take for granted, take on, take over, take up, put on, get into.