Flowing fluid past curved objects has been used for centuries to power rotary motion in man-made machines. In contrast, rotary motion in nanoscale biological, or chemical systems is produced by biasing Brownian motion through cyclic chemical reactions. Here, we show that a curved biological molecule, a DNA or RNA duplex, rotates, uni- directionally, billions of revolutions per minute when electric field is applied along the duplex, with the rotation direction being determined by the duplex chirality. The rotation is found to be powered by the drag force of the electro-osmotic flow, realizing the operating principle of a macroscopic turbine at the nanoscale. The resulting torques are sufficient to power rotation of nanoscale beads and rods, offering an engineering principle for constructing nanoscale systems powered by electric field.