Yes, rim is a Scrabble word!
...and is worth 5 points in Scrabble, and 6 points in Words with Friends
rim
Verb
1. Run around the rim of
2. Furnish with a rim
3. Roll around the rim of
Noun
1. The shape of a raised edge of a more or less circular object
2. (basketball) the hoop from which the net is suspended
3. The outer part of a wheel to which the tire is attached
4. A projection used for strength or for attaching to another object
5. The top edge of a vessel or other container
What Scrabble words can I make with the letters in rim?
3 Letter Words
2 Letter Words