Drag reduction in two-dimensional flow over a circular cylinder, achieved using rotary oscillation, was investigated with computational simulations. In the experiments of Tokumaru & Dimotakis (1991), this mechanism was observed to yield up to 80% drag reduction at Re = 15 000 for certain ranges of frequency and amplitude of sinusoidal rotary oscillation. Simulations with a high-resolution viscous vortex method were carried out over a range of Reynolds numbers (150–15 000) to explore the effects of oscillatory rotational forcing. Significant drag reduction was observed for a rotational forcing which had been very effective in the experiments. The impact of the forcing is strongly Reynolds number dependent. The cylinder oscillation appears to trigger a distinctive shedding pattern which is related to the Reynolds number dependence of the drag reduction. It appears that the source of this unusual shedding pattern and associated drag reduction is vortex dynamics in the boundary layer initiated by the oscillatory cylinder rotation. The practical efficiency of the drag reduction procedure is also discussed.