Bed load sediment transport, in which wind or water flowing over a bed of sediment causes grains to roll or hop along the bed, is a critically important mechanism in contexts ranging from river restoration to planetary exploration. Despite its widespread occurrence, predictions of bed load sediment flux are notoriously imprecise. Many studies have focused on grain size variability as a source of uncertainty, but few have investigated the role of grain shape, even though shape has long been suspected to influence transport rates. Here we show that grain shape can modify bed load transport rates by an amount comparable to the scatter in many sediment transport data sets. We develop a theory that accounts for grain shape effects on fluid drag and granular friction and predicts that the onset and efficiency of bed load transport depend on the mean drag coefficient and bulk friction coefficient of the transported grains. Laboratory flume experiments using a variety of grain shapes confirm these predictions. We propose a shape-independent sediment transport law that collapses our experimental measurements onto a single trend, allowing for more accurate predictions of sediment transport and helping reconcile theory developed for spherical particle transport with the behavior of natural sediment grains.