The physical circulation of the Southern Ocean sets the surface concentration and thus air-sea exchange of CO₂.  However, we have a limited understanding of the three-dimensional circulation that brings deep carbon-rich waters to the surface. Here, we introduce and analyze a novel high-resolution ocean model simulation with active biogeochemistry and online Lagrangian particle tracking. We focus our attention on a subset of particles with high dissolved inorganic carbon (DIC) that originate below 1,000 m and eventually upwell into the near-surface layer (upper 200 m). We find that 71% of the DIC-enriched water upwelling across 1,000 m is concentrated near topographic features, which occupy just 33% of the Antarctic Circumpolar Current. Once particles upwell to the near-surface layer, they exhibit relatively uniform _pCO₂ levels and DIC decorrelation timescales, regardless of their origin. Our results show that Southern Ocean bathymetry plays a key role in delivering carbon-rich waters to the surface.