Yes, INVENTORY is a Scrabble word!

Letter values in Scrabble US: I 1, N 1, V 4, E 1, N 1, T 1, O 1, R 1, Y 4.

Is it a valid word?

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

a detailed list of all the items in stock
the merchandise that a shop has on hand
(accounting) the value of a firm's current assets including raw materials and work in progress and finished goods
a collection of resources
making an itemized list of merchandise or supplies on hand

Also: stock list, stock-taking, take stock, stock-take.