The tropics have been suggested as the drivers of global ocean and atmosphere circulation and biogeochemical cycling during the extreme warmth of the Cretaceous period; but the links between orbital forcing, freshwater runoff and the biogeochemistry of continental margins in extreme greenhouse conditions are not fully understood. Here we present Cretaceous records of geochemical tracers for freshwater runoff obtained from a sediment core off the Ivory Coast that indicate that alternating periods of arid and humid African climate were driven by orbital precession. Our simulations of the precession-driven patterns of river discharge with a global climate model suggest that ocean anoxia and black shale sedimentation were directly caused by high river discharge, and occurred specifically when the northern equinox coincided with perihelion (the minimum distance between the Sun and the Earth). We conclude that, in a warm climate, the oceans off tropical continental margins respond rapidly and sensitively to even modest changes in river discharge.