We report a soft actuator that generates continuous rotation of an object placed on it by electromagnetically exciting circular travelling waves in a soft disk. The disk, that serves as the stator, is made of a stretchable composite consisting of segments of silicone elastomer in which hard ferromagnetic particles are embedded. Inspired by piezoelectric traveling wave rotary actuators, the disk's 16 sections are driven by underlying printed circuit board coils to create a flexural traveling wave on the disk's surface. The rotor can be any object directly placed on the stator: the traveling wave in the stator leads by friction to the rotation of the rotor. Unlike conventional electromagnetic motors that rely on a precisely controlled gap between stator and rotor, a concept incompatible with soft robotics, our device exploits the contact between rotor and stator and the associated dry friction to generate torque. Rotation speeds of over 6 rpm were obtained for a partially rice-filled balloon, 30 cm diameter, weighing 17 g. We report detailed speed and performance metrics when rotating plastic disks. With this rotating actuator, we demonstrate an innovative way to transmit torques and rotations within soft structures.