There are some shops that do this. It's about $70 per day to rent a basic camera, i.e. without strobes, etc.
I wouldn't really recommend it. It takes some time working with your camera to get the settings right and learn to change them for different conditions. Most people don't want to spend their precious underwater time messing around with the camera settings.
LeisurePro.com has a few underwater point and shoot cameras and disposable cameras that work pretty well. There is one disposable which is rated to 45 feet that you can reload and reuse use several times, if you open it carefully.