Yes, HIGH is a Scrabble word!

Letter values in Scrabble US: H 4, I 1, G 2, H 4.

Is it a valid word?

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

a lofty level or position or degree
an air mass of higher than normal pressure
a state of sustained elation
a state of altered consciousness induced by alcohol or narcotics
a high place
a public secondary school usually including grades 9 through 12
a forward gear with a gear ratio that gives the greatest vehicle velocity for a given engine speed

greater than normal in degree or intensity or amount
(literal meaning) being at or having a relatively great or specific elevation or upward extension (sometimes used in combinations like `knee-high')
standing above others in quality or position
used of sounds and voices; high in pitch or frequency
happy and excited and energetic
(used of the smell of meat) smelling spoiled or tainted
slightly and pleasantly intoxicated from alcohol or a drug (especially marijuana)

Also: senior high school, senior high, high school, high gear, high-pitched, in high spirits, high up.

Not playable in Scrabble US: HIGHSCHOOL.