Raman scattering with regard to circularly polarized incident and scattered lights is closely related to the circular activity of a given system. We investigate the symmetry of its activity, called the cross-circular and parallel-circular Raman optical activity. The analysis is systematically performed with the magnetic point groups, and it indicates that the response allows for a useful diagnosis of the symmetry of materials such as chirality and (magneto)axiality. It is also shown that the Stokes and anti-Stokes processes are related to each other by the conserved antiunitary symmetry, which can be either the time-reversal operation or the combination of time-reversal and mirror reflection.

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• Crystal symmetry
• Optical activity
• Chiral symmetry
• Raman spectroscopy