Totten Glacier in East Antarctica has the potential to raise global sea level by at least 3.5 m, but its sensitivity to climate change has not been well understood. The glacier is coupled to the ocean by the Totten Ice Shelf, which has exhibited variable speed, thickness, and grounding line position in recent years. To understand the drivers of this interannual variability, we compare ice velocity to oceanic wind stress and find a consistent pattern of ice-shelf acceleration 19 months after upwelling anomalies occur at the continental shelf break nearby. The sensitivity to climate forcing we observe is a response to wind-driven redistribution of oceanic heat and is independent of large-scale warming of the atmosphere or ocean. Our results establish a link between the stability of Totten Glacier and upwelling near the East Antarctic coast, where surface winds are projected to intensify over the next century as a result of increasing atmospheric greenhouse gas concentrations.