Yes, CONSTRUCTED is a Scrabble word!

Letter values in Scrabble US: C 3, O 1, N 1, S 1, T 1, R 1, U 1, C 3, T 1, E 1, D 2.

Is it a valid word?

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

make by combining materials and parts
put together out of artificial or natural components or parts; He manufactured a popular cereal"
draw with suitable instruments and under specified conditions
create by linking linguistic units
create by organizing and linking ideas, arguments, or concepts
reassemble mentally