Yes, ASSIGNMENT is a Scrabble word!

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

Is it a valid word?

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

a duty that you are assigned to perform (especially in the armed forces)
the instrument by which a claim or right or interest or property is transferred from one person to another
the act of distributing something to designated places or persons
(law) a transfer of property by deed of conveyance
an undertaking that you have been assigned to do (as by an instructor)
the act of putting a person into a non-elective position

Also: duty assignment.