Yes, WASHING is a Scrabble word!

Letter values in Scrabble US: W 4, A 1, S 1, H 4, I 1, N 1, G 2.

Is it a valid word?

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

clean with some chemical process
cleanse (one's body) with soap and water
cleanse with a cleaning agent, such as soap, and water
move by or as if by water
be capable of being washed
admit to testing or proof
separate dirt or gravel from (precious minerals)
apply a thin coating of paint, metal, etc., to
remove by the application of water or other liquid and soap or some other cleaning agent
form by erosion
make moist
wash or flow against
to cleanse (itself or another animal) by licking

Also: wash out, wash off, wash away.