Yes, SIGNED is a Scrabble word!

Letter values in Scrabble US: S 1, I 1, G 2, N 1, E 1, D 2.

Is it a valid word?

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

mark with one's signature; write one's name (on)
approve and express assent, responsibility, or obligation
be engaged by a written agreement
engage by written agreement
communicate silently and non-verbally by signals or signs
place signs, as along a road
communicate in sign language
make the sign of the cross over someone in order to call on God for protection; consecrate

Also: sign on, sign up, sign-language.