We present a theoretical study of pump-induced Faraday and Kerr rotation in a two-dimensional lattice of conducting disks. We propose a mechanism of Faraday and Kerr responses in which a circularly polarized pump directly induces a high-frequency Hall component σ_xy=-σ_yx of the electron conductivity tensor at the probe frequency. Microscopically, σ_xy originates from the third-order nonlinear response of the electron gas rather than from the real magnetic field created by solenoidal charge currents in the inverse Faraday effect. We show that the Faraday and Kerr rotation angles are significantly enhanced when the pump and probe frequencies are tuned close to the plasmon resonance of the disks, reaching ∼ 0.1^∘ per 1 kW/cm² of incident pump intensity in the terahertz range. This mechanism can explain recently observed giant pump-induced Faraday rotation in graphene disk lattices.