Yes, FRIGIDITY is a Scrabble word!

Letter values in Scrabble US: F 4, R 1, I 1, G 2, I 1, D 2, I 1, T 1, Y 4.

Is it a valid word?

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

sexual unresponsiveness (especially of women) and inability to achieve orgasm during intercourse
the absence of heat
a lack of affection or enthusiasm

Also: low temperature.