Yes, cheer is a Scrabble word!

Verb

1. Give encouragement to

2. Show approval or good wishes by shouting

3. Cause (somebody) to feel happier or more cheerful

4. Become cheerful

5. Spur on or encourage especially by cheers and shouts

Noun

1. A cry or shout of approval

2. The quality of being cheerful and dispelling gloom