The Southern Ocean is the largest sink of anthropogenic carbon in the present-day climate. Here, Southern Ocean 𝑝CO2 and its dependence on wind forcing are investigated using an equilibrium mixed layer carbon budget. This budget is used to derive an expression for Southern Ocean 𝑝CO2 sensitivity to wind stress. Southern Ocean 𝑝CO2 is found to vary as the square root of area-mean wind stress, arising from the dominance of vertical mixing over other processes such as lateral Ekman transport. The expression for p\hbox {CO}_{2} is validated using idealised coarse-resolution ocean numerical experiments. Additionally, we show that increased (decreased) stratification through surface warming reduces (increases) the sensitivity of the Southern Ocean 𝑝CO2 to wind stress. The scaling is then used to estimate the wind-stress induced changes of atmospheric 𝑝CO2 in CMIP5 models using only a handful of parameters. The scaling is further used to model the anthropogenic carbon sink, showing a long-term reversal of the Southern Ocean sink for large wind stress strength.