We investigate the influence of magnetic fields on the electron-positron pair equilibrium in an optically thin relativistic plasma. We assume that the plasma is uniform and static with a proton density N and a size R and that magnetic fields are randomly oriented. We found that qualitative features are similar to those of a plasma without magnetic fields; there exist two branches of solution for the pair density, and there exist the maximum value attainable of the electron temperature T*≡kTe/mec2 for a given τN≡σTNR, where σT is the Thomson cross section, and the maximum τN allowable for a given T*. With magnetic fields synchrotron-Compton process produces so many hard photons that pair creation rate of photon processes should increase. As a result the maximum values of T* and τN decrease and the equilibrium pair density decreases (increases) for the higher (lower) branch solution. It is found that these effects are significant, even if the magnetic energy density is below the equipartition value by several orders of magnitude.