Despite motion on the retina with every saccade, we perceive the world as stable. But whether this stability is a result of neurons constructing a spatial map or continually remapping a retinal representation is unclear. Previous work has focused on the perceptual consequences of shifts in the horizontal and vertical dimensions, but torsion is another key component in ocular orienting that – unlike horizontal and vertical movements – produces a natural misalignment between spatial and retinal coordinates. Here we took advantage of oblique eye orientation-induced retinal torsion to examine perisaccadic orientation perception. We found that orientation perception was largely predicted by the retinal image throughout each trial. Surprisingly however, we observed a significant presaccadic remapping of the percept consistent with maintaining a stable (but spatially inaccurate) retinotopic perception throughout the saccade. These findings strongly suggest that our seamless perceptual stability relies on retinotopic signals that are remapped with each saccade.