The Southern Ocean carbon sink accounts for 40% of the global ocean carbon think making its future evolution crucial for understanding and quantifying climate change. State-of-the-art estimates of the future carbon sink are provided by earth system models. However, the estimates of the carbon sink are especially uncertain due to biases in the simulation of the complex Southern Ocean overturning circulation. To account for biases in the simulated ocean carbon sink, we used an emergent constraint that corrects the simulated ocean carbon sink for biases in the mode and intermediate water formation in the Southern Ocean (Terhaar et al., 2021). Here, we present the raw simulated annual global ocean carbon sink estimates for three future scenarios of CMIP5 and CMIP6, as well as the unconstrained and constrained estimates of the cumulative Southern Ocean carbon sink from 2000 to 2100.