It is well known that transcription can induce torsional stress in DNA, affecting the activity of nearby genes or even inducing structural transitions in the DNA duplex. It has long been assumed that the generation of significant torsional stress requires the DNA to be anchored, forming a limited topological domain, because otherwise it would spin almost freely about its axis. Previous estimates of the rotational drag have, however, neglected the role of small natural bends in the helix backbone. We show how these bends can increase the drag several thousandfold relative to prior estimates, allowing significant torsional stress even in linear unanchored DNA. The model helps explain several puzzling experimental results on structural transitions induced by transcription of DNA.