Conservation of spin and orbital angular momenta of circularly-polarized vortex light is discussed for Raman spectra of two-dimensional materials. We first show the selection rule for optical absorption of two-dimensional materials as a function of the spin and orbital angular momentum of incident vortex light. In the case of two-dimensional materials, the Raman tensor for the incident vortex light does not change the symmetry of the phonon mode. Furthermore, the Raman active modes are classified by either "helicity-changing" or "helicity-conserved" Raman modes, in which the scattered photon of circularly polarized light either changes or does not change the helicity of the light, respectively. We show tables of selection rules for the Raman active modes of two-dimensional materials with 2, 3, 4, and 6 rotational symmetry for vortex light.