Yes, CITHER is a Scrabble word!

Letter values in Scrabble US: C 3, I 1, T 1, H 4, E 1, R 1.

Is it a valid word?

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

a musical stringed instrument with strings stretched over a flat sounding board; it is laid flat and played with a plectrum and with fingers
a 16th century musical instrument resembling a guitar with a pear-shaped soundbox and wire strings