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Context. Spectropolarimetry of AGNs is a powerful tool for studying the structure and kinematics of the inner regions of quasars. Aims. We wish to investigate the effects of various AGN scattering region geometries on the polarized flux. Methods. We introduce a new, publicly available Monte Carlo radiative transfer code, STOKES, which models polarization induced by scattering off free electrons and dust grains. We model a variety of regions in AGNs. Results. We find that the shape of the funnel of the dusty torus has a significant impact on the polarization efficiency. A compact torus with a steep inner surface scatters more light toward type-2 viewing angles than a large torus of the same half-opening angle, Ө0. For Ө0 < 53°, the scattered light is polarized perpendicularly to the symmetry axis, whilst for Ө0 > 60° it is polarized parallel to the symmetry axis. In between these intervals the orientation of the polarization depends on the viewing angle. The degree of polarization ranges between 0% and 20% and is wavelength independent for a large range of Ө0. Observed wavelength-independent optical and near-UV polarization thus does not necessarily imply electron scattering. Spectropolarimetry at rest-frame wavelengths less than 2500 Å may distinguish between dust and electron scattering but is not conclusive in all cases. For polar dust, scattering spectra are reddened for type-1 viewing angles, and made bluer for type-2 viewing angles. Polar electron-scattering cones are very efficient polarizers at type-2 viewing angles, whilst the polarized flux of the torus is weak. Conclusions. We predict that the net polarization of Seyfert-2 galaxies decreases with luminosity, and conclude that the degree of polarization should be correlated with the relative strength of the thermal IR flux. We find that a flattened, equatorial, electron-scattering disk, of relatively low optical depth, reproduces type-1 polarization. This is insensitive to the exact geometry, but the observed polarization requires a limited range of optical depth.