Is it normal for my arms to get numb while I am sleeping?

No, unless .. If you are sleeping on them, you may cause numbness due to pressure on the nerve/blood vessel plexus. This should reverse quickly. If you are not sleeping on them, see a neurologist for evaluation.
Yes. If pregnant, it is very common for hands to become numb secondary to temporary carpal tunnel syndrome. The best cure for this would be to wear wrist splints like those worn during roller blading. This will put your wrists in an anatomically neutral position, allowing the best blood flow, decreasing pain and numbness until after delivery.