Answer:
Yes, you actually could receive a degree in medieval torture. There are a number of colleges that allow students to design their own programs, leading to a number of degrees in unique majors. Also, it is possible to get a doctorate in an area of study for which no doctorate has ever previously been granted, and I have known three different people who had unique doctorates. If you are planning on doing this with real, accredited schools, however, be prepared to spend a lot of money doing it.