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In this paper, we present a novel rotating actuator based on the interaction of a permanent magnet with a magnetostrictive soft ribbon submitted to mechanical stress. The direction and magnitude of the stress generates a directional magnetic anisotropy (easy axis) in the soft ribbon. A nonzero angle between the polarizing magnet and the induced easy axis results in a torque between the two: hence the magnet being free to rotate aligns itself with the easy axis. A demonstrator of this principle was made using a Nd-Fe-B magnet above a disk cut from an iron-based amorphous ribbon glued between two unidirectional piezoelectric actuators. The analytical model takes into account the magnetic domains and assumes a magnetization mechanism of both coherent rotation and domain-wall displacement, with a uniaxial anisotropy induced by the applied stress.