Uptake of 13C-depleted anthropogenic carbon dioxide in the surface ocean may eliminate or reverse the natural vertical gradient in the isotopic composition of dissolved inorganic carbon in the ocean, analogous to events at the Paleocene-Eocene Thermal Maximum, suggest ocean model simulations. Paleoceanographic records suggest that the present-day vertical gradient in the stable carbon isotopic composition (delta C-13) of dissolved inorganic carbon in the ocean was reversed during the Paleocene-Eocene Thermal Maximum, an early period of relatively rapid release of carbon into the climate system. Here we present simulations from an observationally constrained ocean model under various greenhouse gas emissions scenarios. We project a decrease in the globally averaged delta C-13 of dissolved inorganic carbon in the surface ocean of between -1.8 to -6.3 parts per thousand by 2100. This reduction is driven by oceanic absorption of anthropogenic carbon dioxide, which is depleted in carbon-13. Our findings suggest an elimination or reversal of the natural vertical gradient in the delta C-13 of dissolved inorganic carbon by 2100 unless anthropogenic carbon emissions are reduced soon. We conclude that the Paleocene-Eocene Thermal Maximum is a geologic analogue of future global carbon cycle perturbations under continued rapid anthropogenic carbon emissions.