Yes, WEAVER is a Scrabble word!

Letter values in Scrabble US: W 4, E 1, A 1, V 4, E 1, R 1.

Is it a valid word?

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

a craftsman who weaves cloth
finch-like African and Asian colonial birds noted for their elaborately woven nests

Also: weaver finch.