Yes, STUDYING is a Scrabble word!

Letter values in Scrabble US: S 1, T 1, U 1, D 2, Y 4, I 1, N 1, G 2.

Is it a valid word?

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

consider in detail and subject to an analysis in order to discover essential features or meaning
be a student; follow a course of study; be enrolled at an institute of learning
give careful consideration to
be a student of a certain subject
learn by reading books; I must hit the books now"
think intently and at length, as for spiritual purposes

Also: poring over, hit the books.