Yes, BUCKTHORNS is a Scrabble word!

Letter values in Scrabble US: B 3, U 1, C 3, K 5, T 1, H 4, O 1, R 1, N 1, S 1.

Is it a valid word?

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

a shrub or shrubby tree of the genus Rhamnus; fruits are source of yellow dyes or pigments
any shrub or small tree of the genus Bumelia
an Old World plantain with long narrow ribbed leaves widely established in temperate regions

Also: english plantain, narrow-leaved plantain, ripple-grass, plantago lanceolata.