In order to reverse the magnetization of small ferromagnetic particles it is necessary to overcome an energy barrier, which is mainly defined by the magnetic anisotropy. Usual reversal stimuli include the application of static or time-dependent external magnetic fields, thermal activation, spin transfer torque, or combinations thereof. Here, we report on repeated, quasi-periodic magnetization reversal in single-domain particles that are exposed to a constant magnetic field perpendicular to the magnet's easy axis. The continuous sequence of reversals is induced by torsional oscillations of the magnet's anisotropy landscape, which are caused by angular oscillations of the magnet's body. In our experiments, a nickel nanowire constitutes both a mechanical resonator and a nanomagnetic sample with uniaxial anisotropy. We measure the transient flexural vibration behavior by electron beam based methods and find strong signatures of periodic magnetization switching between two magnetic states of the nanowire. Our system can be modeled as a driven damped harmonic oscillator under the influence of switchable magnetostatic interactions.