Mechanical interactions between cells play a fundamental role in the self-organization of organisms. How these interactions drive coordinated cell movement in three dimensions remains unclear. Here we report that cell doublets embedded in a three-dimensional extracellular matrix undergo spontaneous rotations. We investigate the rotation mechanism and find that it is driven by a polarized distribution of myosin within cell cortices. The mismatched orientation of this polarized distribution breaks the doublet mirror symmetry. In addition, cells adhere at their interface through adherens junctions and with the extracellular matrix through focal contacts near myosin clusters. We use a physical theory describing the doublet as two interacting active surfaces to show that rotation is driven by myosin-generated gradients of active tension whose profiles are dictated by interacting cell polarity axes. We also show that three-dimensional shape symmetries are related to broken symmetries of the myosin distribution in cortices. To test for the rotation mechanism, we suppress myosin clusters using laser ablation and generate new myosin clusters by optogenetics. Our work clarifies how polarity-oriented active mechanical forces drive collective cell motion in three dimensions.