A suite of observations suggests that the northern plains of Mars, which cover nearly one third of the planet's surface, may once have contained an ocean. Perhaps the most provocative evidence for an ancient ocean is a set of surface features that ring the plains for thousands of kilometres and that have been interpreted as a series of palaeoshorelines of different age. It has been shown, however, that topographic profiles along the putative shorelines contain long-wavelength trends with amplitudes of up to several kilometres, and these trends have been taken as an argument against the martian shoreline (and ocean) hypothesis. Here we show that the long-wavelength topography of the shorelines is consistent with deformation caused by true polar wander--a change in the orientation of a planet with respect to its rotation pole--and that the inferred pole path has the geometry expected for a true polar wander event that postdates the formation of the massive Tharsis volcanic rise.