Is their a word in the Scrabble Dictionary

Yes, their is playable

...and is worth 7 points.

Found in the following dictionaries

Enable (Words with friends)
SOWPODS (Collins Scrabble Words)
OTCWL2014 (NASPA Word List 2014)
TWL06 (NASPA List 2006)

"Their" Definition

adjective

Usage Problem His, her, or its: "It is fatal for anyone who writes to think of their sex” ( Virginia Woolf). See Usage Notes at he1, they.
Used as a modifier before a noun: their accomplishments; their home town.
Of or relating to them or themselves especially as possessors, , or objects of an action .
His or her .