A circularly polarized light can induce a dissipationless dc current in a quantum nanoring which is responsible for a resonant helicity-driven contribution to magnetic moment. This current is not suppressed by thermal averaging despite its quantum nature. We refer to this phenomenon as the quantum resonant inverse Faraday effect. For weak electromagnetic field, when the characteristic coupling energy is small compared to the energy level spacing, we predict narrow resonances in the circulating current and, consequently, in the magnetic moment of the ring. For strong fields, the resonances merge into a wide peak with a width determined by the spectral curvature. We further demonstrate that weak short-range disorder splits the resonances and induces additional particularly sharp and high resonant peaks in dc current and magnetization. In contrast, long-range disorder leads to a chaotic behavior of the system in the vicinity of the separatrix that divides the phase space of the system into regions with dynamically localized and delocalized states.
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