Tried to find it online, but nothing. Everyone refers to it and that it's named after the famous James Clerk Maxwell (of the Maxwell electromagnetic laws and some other things), but there is no direct reference, and it's like the experiment has always been done (although you need some concepts of rigid bodies to do it).
If you don't remember, the Maxwell's wheel is a classic mechanics experiment that is usually done in college laboratory practices. The experiment consists of a wheel with a bar through its radius that is hung on two different threads, one at each side. If you roll upwards the threads turning the wheel and then release it all the potential energy of the wheel converts to Kinetic energy of movement + Kinetic energy of rotation. If you measure falling times for different positions you can get the momentum of inertia of the wheel easily using the principle of conservation of energy.
So who came up with it first and when?