Yes, hug is a Scrabble word!
...and is worth 7 points in Scrabble, and 8 points in Words with Friends
hug
Verb
1. Squeeze (someone) tightly in your arms, usually with fondness
2. Fit closely or tightly
Noun
1. A tight or amorous embrace
What Scrabble words can I make with the letters in hug?
3 Letter Words
2 Letter Words