Verified answer

Try rubbing plain white toothpaste on it. With a soft cloth and a little dab of toothpaste, gently buff the disc and then let it set for about 5 minutes. Then run the disc under some cold water and wash all of the toothpaste off. Let the disc air dry, or use another clean, dry soft cloth to dry it off. Once it's completely dry, try it in the Xbox 360 again.

Toothpaste is a mild abrasive and will help "sand" down some of the scratches and might restore your disc back to a usable condition.