The recent surge of megathrust earthquakes and tsunami disasters has highlighted the need for a comprehensive understanding of earthquake cycles along convergent plate boundaries. Space geodesy has been used to document recent crustal deformation patterns with unprecedented precision, however the production of long paleogeodetic records of vertical seafloor motion is still a major challenge. Here we show that carbon isotope ratios (δC13) in the skeletons of massive Porites corals from west Sumatra record abrupt changes in light exposure resulting from coseismic seafloor displacements. Validation of the method is based on the coral δC13 response to uplift (and subsidence) produced by the March 2005 Mw 8.6 Nias-Simeulue earthquake, and uplift further south around Sipora Island during a M~8.4 megathrust earthquake in February 1797. At Nias, the average step-change in coral δC13 was 0.6±0.1‰/m for coseismic displacements of +1.8 m and -0.4 m in 2005. At Sipora, a distinct change in Porites microatoll growth morphology marks coseismic uplift of 0.7 m in 1797. In this shallow water setting, with a steep light attenuation gradient, the step-change in microatoll δC13 is 2.3‰/m, nearly four times greater than for the Nias Porites. Considering the natural variability in coral skeletal δC13, we show that the lower detection limit of the method is around 0.2 m of vertical seafloor motion. Analysis of vertical displacement for well-documented earthquakes suggests this sensitivity equates to shallow events exceeding Mw~7.2 in central megathrust and back-arc thrust fault settings. Our findings indicate that the coral C13/C12 paleogeodesy technique could be applied to convergent tectonic margins throughout the tropical western Pacific and eastern Indian oceans, which host prolific coral reefs, and some of the world's greatest earthquake catastrophes. While our focus here is the link between coral δC13, light exposure and coseismic crustal deformation, the same principles could be used to characterize interseismic strain during earthquake cycles over the last several millennia.