In this study, we explore the impact of strong magnetic fields on the masses and radii of oblate spheroidal white dwarfs, using the parameterized \(\gamma \) -metric formalism to account for deformation caused by anisotropic pressures. A relativistic free Fermi gas of electrons at absolute zero temperature is modeled with strong magnetic field which introduce anisotropy between pressures parallel and perpendicular to its direction. This anisotropy arises due to the breaking of O(3) rotational symmetry due to strong magnetic field, leading to the deformation of the white dwarfs into oblate spheroids and enables the existence of stable super-Chandrasekhar white dwarfs with masses exceeding \(5M_{\odot }\) . Our results show that, at a fixed central density, the mass is observed to initially increase with increase in central magnetic field and then decrease for high magnetic fields, while the equatorial radius increases with increasing magnetic field strength. At very low magnetic fields, the traditional Chandrasekhar mass limit is recovered. We also found that, the maximum mass is observed to occur at lower central energy densities for lower magnetic fields and at higher central energy densities as the magnetic field strength increases. These results indicate that the pressure anisotropy caused by strong magnetic fields soften the equation of state (EoS), resulting the stars to become more compact.