Flow-driven rotary motors such as windmills and water wheels drive functional processes in human society. Although examples of such rotary motors also feature prominently in cell biology, their synthetic construction at the nanoscale has remained challenging. Here we demonstrate flow-driven rotary motion of a self-organized DNA nanostructure that is docked onto a nanopore in a thin solid-state membrane. An elastic DNA bundle self-assembles into a chiral conformation upon phoretic docking onto the solid-state nanopore, and subsequently displays a sustained unidirectional rotary motion of up to 20 rev s⁻¹. The rotors harness energy from a nanoscale water and ion flow that is generated by a static chemical or electrochemical potential gradient in the nanopore, which are established through a salt gradient or applied voltage, respectively. These artificial nanoengines self-organize and operate autonomously in physiological conditions, suggesting ways to constructing energy-transducing motors at nanoscale interfaces.