A novel wrist-inspired soft actuator, which is driven by a magneto-pneumatic hybrid system and based on a Kresling origami unit, is proposed. The geometric model, kinematic analysis model, and quasistatic analysis model of the Kresling origami unit are presented. A key focus is on the formulation and investigation of the variation in rotation angle using the kinematic analysis model. A wrist-inspired soft actuator is designed, and its quasistatic characteristics are validated through various experiments. The paper proposes an innovative magneto-pneumatic hybrid actuation method, capable of achieving bidirectional torsion. This actuation method is experimentally validated, demonstrating the actuator's ability to maintain 3 steady states and its capability for bidirectional torsion deformation. Furthermore, the paper highlights the potential of the Kresling origami unit in designing soft actuators capable of achieving large rotation angles. For instance, an actuator with 6 sides ( n = 6) is shown to achieve a rotation angle of 239.5°, and its rotation ratio exceeds 277°, about twice the largest one reported in other literature. The actuator offers a practical and effective solution for bidirectional torsion deformation in soft robotic applications.