One of the most dramatic perturbations to the Earth system during the past 100 million years was the rapid onset of Antarctic glaciation near the Eocene/Oligocene epoch boundary (approximately 34 million years ago). This climate transition was accompanied by a deepening of the calcite compensation depth--the ocean depth at which the rate of calcium carbonate input from surface waters equals the rate of dissolution. Changes in the global carbon cycle, rather than changes in continental configuration, have recently been proposed as the most likely root cause of Antarctic glaciation, but the mechanism linking glaciation to the deepening of calcite compensation depth remains unclear. Here we use a global biogeochemical box model to test competing hypotheses put forward to explain the Eocene/Oligocene transition. We find that, of the candidate hypotheses, only shelf to deep sea carbonate partitioning is capable of explaining the observed changes in both carbon isotope composition and calcium carbonate accumulation at the sea floor. In our simulations, glacioeustatic sea-level fall associated with the growth of Antarctic ice sheets permanently reduces global calcium carbonate accumulation on the continental shelves, leading to an increase in pelagic burial via permanent deepening of the calcite compensation depth. At the same time, fresh limestones are exposed to erosion, thus temporarily increasing global river inputs of dissolved carbonate and increasing seawater delta13C. Our work sheds new light on the mechanisms linking glaciation and ocean acidity change across arguably the most important climate transition of the Cenozoic era.