Yes, rim is a Scrabble word!

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