We investigate the impact of century-scale climate changes on the Southern Ocean CO2 sink using an idealized ocean general circulation and biogeochemical model. The simulations are executed under both constant and changing wind stress, freshwater fluxes, and atmospheric pCO2, so as to separately analyze changes in natural and anthropogenic CO2 fluxes under increasing wind stress and stratification. We find that the Southern Ocean sink for total contemporary CO2 is weaker under increased wind stress and stratification by 2100, relative to a control run with no change in physical forcing, although the results are sensitive to the magnitude of the imposed physical changes and the rate of increase of atmospheric pCO2. The air-sea fluxes of both natural and anthropogenic CO2 are sensitive to the surface concentration of dissolved inorganic carbon (DIC) which responds to perturbations in wind stress and stratification differently. Spatially averaged surface DIC scales linearly with wind stress, primarily driven by changes in the Ekman transport. In contrast, changes in the stratification cause non-linear and more complex responses in spatially averaged surface DIC, involving shifts in the location of isopycnal outcrop for deep and thermocline waters. Thus, it is likely that both wind stress and stratification changes will influence the strength of the Southern Ocean CO2 sink in the coming century.