Yes, CENTRE is a Scrabble word!

Letter values in Scrabble US: C 3, E 1, N 1, T 1, R 1, E 1.

Is it a valid word?

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

a low-lying region in central France
an area that is approximately central within some larger region
a point equidistant from the ends of a line or the extremities of a figure
a place where some particular activity is concentrated
the sweet central portion of a piece of candy that is enclosed in chocolate or some other covering
the choicest or most essential or most vital part of some idea or experience
the object upon which interest and attention focuses
a cluster of nerve cells governing a specific bodily process
a building dedicated to a particular activity

Also: heart and soul, nitty-gritty, center of attention, centre of attention, nerve center, nerve centre.