The present work incorporates a modified Q-state Monte Carlo (Potts) model to evaluate two-dimensional annealing of representative paramagnetic and diamagnetic polycrystalline materials in the presence of a magnetic field. Anisotropies in grain boundary energy, caused by differences in grain orientation (texturing), and the presence of an external magnetic field are examined in detail. In the former case, the Read–Shockley equations are used, in which grain boundary energies are computed using a low-angle misorientation approximation. In the latter case, magnetic anisotropy is simulated based on the relative orientation between the principal grain axis and the external magnetic field vector. Among other findings, the results of texture development subject to a magnetic field showed an increasing orientation distribution function (ODF) asymmetry over time, with higher intensities favoring the grains with principal axes most closely aligned with the magnetic field direction. The magnetic field also tended to increase the average grain size, which was accompanied by a corresponding decrease in the total grain boundary energy.