Yes, UNIT is a Scrabble word!

Letter values in Scrabble US: U 1, N 1, I 1, T 1.

Is it a valid word?

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

any division of quantity accepted as a standard of measurement or exchange
an individual or group or structure or other entity regarded as a structural or functional constituent of a whole
an organization regarded as part of a larger social group
a single undivided whole
a single undivided natural thing occurring in the composition of something else
an assemblage of parts that is regarded as a single entity

Also: unit of measurement, social unit, building block.