Soft actuators allow to transform external stimuli to mechanical deformations. Because of their deformational response to external magnetic fields, magnetic gels and elastomers represent ideal candidates for such tasks. Mostly, linear magnetostrictive deformations, that is, elongations or contractions along straight axes are discussed in this context. In contrast to that, we here suggest to realize a twist actuator that responds by torsional deformations around the axis of the applied magnetic field. For this purpose, we theoretically investigate the overall mechanical response of a basic model system containing discrete magnetizable particles in a soft elastic matrix. Two different types of discrete particle arrangements are used as starting conditions in the nonmagnetized state. These contain globally twisted anisotropic particle arrangements on the one hand, and groups of discrete helical-like particle structures positioned side by side on the other hand. Besides the resulting twist upon magnetization, we also evaluate different other modes of deformation. Our analysis supports the construction of magnetically orientable and actuatable torsional mixing devices in fluidic applications or other types of soft actuators that initiate relative rotations between different components.