This will depend on the terms of the restitution judgment and the statute under which it was awarded. It may be possible to return to the court to request this relief.
Most states bar convicted persons from making any profits from their crimes and mandate that if restitution is due. These "Son of Sam" laws typically require the proceeds to be paid to the victim (some require separate civil lawsuits). I've also added a relevent link from the National Center for Victims Rights.