Yes, ROUTERS is a Scrabble word!

Letter values in Scrabble US: R 1, O 1, U 1, T 1, E 1, R 1, S 1.

Is it a valid word?

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

a worker who routes shipments for distribution and delivery
(computer science) a device that forwards data packets between computer networks
a power tool with a shaped cutter; used in carpentry for cutting grooves