Polarization of radiation emerging from magnetized, electron-scattering-dominated accretion discs in active galactic nuclei (AGN) may be strongly affected by Faraday rotation. We present fully self-consistent Monte Carlo calculations of the resulting polarization in plane-parallel electron-scattering atmospheres for magnetic fields of constant strength and both vertical and random topology. We provide analytic fits to our results and apply them to simple accretion disc models. We find that Faraday rotation by an equipartition magnetic field may be of major importance in determining the polarization at optical and ultraviolet wavelengths in AGN. It may also be important for future X-ray polarization measurements of black hole candidate X-ray binaries.