An optically and geometrically thick torus obscures the central engine of active galactic nuclei (AGN) from some lines of sight. From a magnetohydrodynamical framework, the torus can be considered to be a particular region of clouds surrounding the central engine where the clouds are dusty and optically thick. In this framework, the magnetic field plays an important role in the creation, morphology and evolution of the torus. If the dust grains within the clouds are assumed to be aligned by paramagnetic alignment, then the ratio of the intrinsic polarization and visual extinction, P(per cent)/Av, is a function of the magnetic field strength. To estimate the visual extinction through the torus and constrain the polarization mechanisms in the nucleus of the type 2 AGN, IC 5063, we developed a polarization model to fit both the total and polarized flux in a 1.2-arcsec (˜263 pc) aperture. The polarization model is consistent with the nuclear polarization observed at Kn (2.0-2.3 μm) being produced by dichroic absorption from aligned dust grains with a visual extinction through the torus of 48 ± 2 mag. We estimated the intrinsic polarization arising from dichroic absorption to be P^{{dic}}_{{{K_n}}} = 12.5 ± 2.7 per cent. We consider the physical conditions and environment of the gas and dust for the torus of IC 5063. Then, through paramagnetic alignment, we estimate a magnetic field strength in the range of 12-128 mG in the near-infrared emitting regions of the torus of IC 5063. Alternatively, we estimate the magnetic field strength in the plane of the sky using the Chandrasekhar-Fermi method. The minimum magnetic field strength in the plane of the sky is estimated to be 13 and 41 mG depending of the conditions within the torus of IC 5063. These techniques afford the chance to make a survey of AGN, to investigate the effects of magnetic field strength on the torus, accretion and interaction to the host galaxy.