Yes, BETTER is a Scrabble word!

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

Is it a valid word?

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

(comparative of `good') superior to another (of the same class or set or kind) in excellence or quality or desirability or suitability; more highly skilled than another
(comparative of `good') changed for the better in health or fitness
(comparative and superlative of `well') wiser or more advantageous and hence advisable
more than half
having desirable or positive qualities especially those suitable for a thing specified
having the normally expected amount
morally admirable
deserving of esteem and respect
promoting or enhancing well-being
agreeable or pleasing
of moral excellence
having or showing knowledge and skill and aptitude
thorough
with or in a close or intimate relationship
financially sound
most suitable or right for a particular purpose
resulting favorably
exerting force or influence
capable of pleasing
appealing to the mind
in excellent physical condition
tending to promote physical well-being; beneficial to health
not forged
not left to spoil
generally admired
in good health especially after having suffered illness or injury; at least I feel well"
resulting favorably
wise or advantageous and hence advisable

comparative of `well'; in a better or more excellent manner or more advantageously or attractively or to a greater degree etc.
from a position of superiority or authority
(often used as a combining form) in a good or proper or satisfactory manner or to a high standard (`good' is a nonstandard dialectal variant for `well')
thoroughly or completely; fully; often used as a combining form
indicating high probability; in all likelihood
(used for emphasis or as an intensifier) entirely or fully
to a suitable or appropriate extent or degree
favorably; with approval
to a great extent or degree
with great or especially intimate knowledge
with prudence or propriety
with skill or in a pleasing manner
in a manner affording benefit or advantage
in financial comfort
without unusual distress or resentment; with good humor

Also: in effect, in force.