ABSTRACT We present radpol – a numerical scheme for integrating multifrequency polarized radiative transfer equations along rays propagating in a curved space–time. The scheme includes radiative processes such as synchrotron emission, absorption, Faraday rotation, and conversion, and, for the first time, relativistic Compton scatterings including effects of light polarization. The scheme is fully covariant and is applicable to model radio-γ-ray emission and its polarization from, e.g. relativistic jets and accretion flows on to black holes and other exotic objects described in alternative metric theories and modelled semi-analytically or with time-dependent magnetohydrodynamical simulations. We perform a few tests to validate the implemented numerical algorithms that handle light polarization in curved space–time. We demonstrate application of the scheme to model broad-band emission spectra from a relativistically hot, geometrically thick coronal-like inflow around a supermassive black hole where the disc model is realized in a general relativistic magnetohydrodynamical simulation.