Axial magnetization changes activated by ac circular magnetic fields in ferromagnetic wires produce transverse hysteresis loops of various shapes, depending on both applied dc longitudinal magnetic field and static torsion. Symmetric magnetization reversals occur when the sample is twisted in zero longitudinal field. The results observed in a partially stress-relieved thin cylindrical Permalloy sample are discussed in terms of coherent rotations of the magnetization within large domains of effective biaxial anisotropy. Considering anisotropic magnetostriction and elastic moduli, a two-dimensional energetic model was used to generate numerically transverse hysteresis loops and time dependence of the axial magnetization and its rate of change, in good qualitative agreement with the experimental data. A quasilinear axial magnetization swing versus applied torsion was observed in circular fields of amplitude around 200 Am−1 if the strain did not exceed 10−4 rad, providing basis for simple and stable small angle transducers.