A primary axiom in geoscience is that the evolution of plants drove global changes in river dynamics. Notably, the apparent sinuosity of rivers, derived from the variance of sediment accretion direction measured in rocks, substantially increased when land plants evolved, around 425 million years ago. This led to the hypothesis that the rise of vegetation triggered river meandering. Recent studies of barren, meandering rivers challenge this notion, but the Paleozoic shift in the geometry of river deposits remains unexplained. Here, we suggest that it occurred because vegetation changes how river bends move through space. Using satellite images to monitor river migration, we found that bank vegetation alters the orientation of point bar accretion, resulting in a 62% increase in the inferred variance of flow direction. These results explain why meandering rivers have been underrecognized in prevegetation stratigraphy.