Yes, CULT is a Scrabble word!

Letter values in Scrabble US: C 3, U 1, L 1, T 1.

Is it a valid word?

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

followers of an exclusive system of religious beliefs and practices
an interest followed with exaggerated zeal
followers of an unorthodox, extremist, or false religion or sect who often live outside of conventional society under the direction of a charismatic leader
a religion or sect that is generally considered to be unorthodox, extremist, or false
a system of religious beliefs and rituals

Also: religious cult.