Yes, ADDICTED is a Scrabble word!

Letter values in Scrabble US: A 1, D 2, D 2, I 1, C 3, T 1, E 1, D 2.

Is it a valid word?

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

to cause (someone or oneself) to become dependent (on something, especially a narcotic drug)