Yes, PROVIDENCE is a Scrabble word!

Letter values in Scrabble US: P 3, R 1, O 1, V 4, I 1, D 2, E 1, N 1, C 3, E 1.

Is it a valid word?

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

the capital and largest city of Rhode Island; located in northeastern Rhode Island on Narragansett Bay; site of Brown University
the guardianship and control exercised by a deity
a manifestation of God's foresightful care for his creatures
the prudence and care exercised by someone in the management of resources

Also: capital of rhode island.