Long-range interactions between quasiparticles give rise to a ‘drag’ that affects the fundamental properties of many systems in condensed matter physics1–11. Drag typically involves the exchange of linear momentum between quasiparticles and strongly influences their transport properties. Here, we describe a kind of drag that involves the exchange of angular momentum between two current-driven magnetic domain walls. The motions of the domain walls are correlated and determined by the strength of the drag. When the drag is below a threshold value, the domain walls move together at a constant intermediate velocity with a steady leakage of angular momentum from the faster to the slower wall. However, we find that when the drag exceeds a threshold value, a different dynamic can take place in which the faster domain wall’s magnetization oscillates synchronously with a precessional motion of the slower domain wall’s magnetization, and angular momentum is continuously transferred between them. Our findings demonstrate a method for delivering spin angular momentum remotely to magnetic entities that otherwise could not be manipulated directly by current, for example, by coupling domain walls or other non-collinear spin textures in metallic and insulating media.