Yes, quit is a Scrabble word!
...and is worth 13 points in Scrabble, and 14 points in Words with Friends
quit
Verb
1. Put an end to a state or an activity
2. Give up or retire from a position
3. Go away or leave
4. Turn away from; give up
5. Give up in the face of defeat of lacking hope; admit defeat
What Scrabble words can I make with the letters in quit?
3 Letter Words
2 Letter Words