What can I do to stop my foot from falling asleep in my cast?

Cast may be tight. If this is constantly happening then your cast may be to tight. Talk to your doctor.
See your doctor. It is not normal for that to happen. It is possible the cast is too high or tight and therefore is compressing a nerve which could result in foot drop. You could also be swelling within the cast. Inform the doctor who applied the cast asap.