Yes, paddle is a Scrabble word!

Verb

1. Propel with a paddle

2. Play in or as if in water, as of small children

3. Swim like a dog in shallow water

4. Walk unsteadily

5. Give a spanking to; subject to a spanking

6. Stir with a paddle

Noun

1. Small wooden bat with a flat surface; used for hitting balls in various games

2. A blade of a paddle wheel or water wheel

3. An instrument of punishment consisting of a flat board

4. A short light oar used without an oarlock to propel a canoe or small boat