Yes, nag is a Scrabble word!
...and is worth 4 points in Scrabble, and 6 points in Words with Friends
nag
Verb
1. Bother persistently with trivial complaints
2. Worry persistently
3. Remind or urge constantly
Noun
1. Someone (especially a woman) who annoys people by constantly finding fault
2. An old or over-worked horse
What Scrabble words can I make with the letters in nag?
3 Letter Words
2 Letter Words