A significant number of intermediate age clusters (1–2 Gyr) in the Magellanic Clouds appear to have multiple stellar populations within them, derived from bimodal or extended main-sequence turn-offs. If this is interpreted as an age spread, the multiple populations are separated by a few hundred million years, which would call into question the long-held notion that clusters are simple stellar populations. Here, we show that stellar rotation in stars with masses between 1.2 and 1.7 M⊙ can mimic the effect of a double or multiple population, whereas in actuality only a single population exists. The two main causes of the spread near the turn-off are the effects of stellar rotation on the structure of the star and the inclination angle of the star relative to the observer. Both effects change the observed effective temperature, hence colour, and flux of the star. In order to match observations, the required rotation rates are 20–50 per cent of the critical rotation, which are consistent with observed rotation rates of similar mass stars in the Galaxy. We provide scaling relations which can be applied to non-rotating isochrones in order to mimic the effects of rotation. Finally, we note that rotation is unlikely to be the cause of the multiple stellar populations observed in old globular clusters, as low-mass stars (<1 M⊙) are not expected to be rapid rotators.