It has been previously suggested that changes in the strength and position of the Southern Hemisphere westerlies could be a key contributor to glacial‐interglacial atmospheric CO2 variations. To test this hypothesis, we perform a series of sensitivity experiments using an Earth system model of intermediate complexity. A strengthening of the climatological mean surface winds over the Southern Ocean induces stronger upwelling and increases the formation of Antarctic Bottom Water. Enhanced Ekman pumping brings more dissolved inorganic carbon (DIC)‐rich waters to the surface. However, the stronger upwelling also supplies more nutrients to the surface, thereby enhancing marine export production in the Southern Hemisphere and decreasing the DIC content in the euphotic zone. The net response is a small atmospheric CO2 increase (∼5 ppmv) compared to the full glacial‐interglacial CO2 amplitude of ∼90 ppmv. Roughly the opposite results are obtained for a weakening of the Southern Hemisphere westerly winds.