Actually, it's probably easier to view it classically.

If you consider just tossing classical particles at the disk, you could do a calculation using conservation of angular momentum for each particle to determine how it effects the disk's rotation. The net effect of many particles would be to sum of the effects of each particle.

EM radiation is a wave distributed over space, but it still carries momentum. Classically speaking, tather than being a bunch of discrete particles, you can treat an EM wave as having a smooth distribution of momentum over space, so that each point in the beam carries a tiny bit of momentum. There's a quantity called the Poynting vector, which basically tells you the momentum of each tiny bit of the beam. If you do the math, you can show that there is a contribution to the Poynting vector from polarization which accounts for the angular momentum of circularly polarized light--this is usually called the spin component of the Poynting vector. (The beam's overall structure, independent of polarization, also contributes to it's momentum distribution, so it can carry an angular momentum that is independent of spin.)

You can always get the right answer for how the disk moves by doing a conservation of angular momentum calculation for each tiny bit of the beam that hits the surface and adding up all the contributions. If the beam hits dead-center along the disk's axis, then you should be able to make a symmetry argument so that you only need to compute a total angular momentum for the beam about its axis, and consider that transferring entirely to the disk.