  We study theoretically the Faraday and Kerr rotation of a probe field due to
the orbital magnetization of a two-dimensional electron gas induced by a
circularly polarized pump. We develop a microscopic theory of these effects in
the intraband spectral range based on the analytical solution of the kinetic
equation for linear and parabolic energy dispersion of electrons and arbitrary
scattering potential. We show that the spectral dependence of rotation angles
and accompanying ellipticities experiences a sharp resonance when the probe and
pump frequencies are close to each other. At the resonance, the Faraday and
Kerr rotation angles are of the order of $0.1^\circ$ per 1~kW/cm$^2$ of the
pump intensity in graphene samples, corresponding to a pump-induced synthetic
magnetic field of about 0.1~T. We also analyze the influence of the dielectric
contrast between dielectric media surrounding the two-dimensional electron gas
on the rotation angles.
