Yes, ROTATIONS is a Scrabble word!

Letter values in Scrabble US: R 1, O 1, T 1, A 1, T 1, I 1, O 1, N 1, S 1.

Is it a valid word?

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

the act of rotating as if on an axis
(mathematics) a transformation in which the coordinate axes are rotated by a fixed angle about the origin
a single complete turn (axial or orbital)
a planned recurrent sequence (of crops or personnel etc.)

Also: rotary motion.