Branching stream networks are a ubiquitous feature of the Earth's surface, but the processes that shape them, and their dependence on the climate in which they grow, remain poorly understood. Research has mainly focused on climatic controls of channel incision rates, while the climatic influence on planform geometry has often been overlooked. Here we analyze nearly one million digitally mapped river junctions throughout the contiguous United States and show that branching angles vary systematically with climatic aridity. In arid landscapes, which are thought to be dominated by surface runoff erosion, junction angles average roughly 45° in the driest places. Branching angles are systematically wider in humid regions, averaging roughly 72°, which is the theoretically predicted angle for network growth in a diffusive field such as groundwater seepage. The correlation of mean junction angle with aridity is stronger than with topographic gradient, downstream concavity, or other geometric factors that have been proposed as controls of junction angles. Thus, it may be possible to identify channelization processes from stream network geometry in relict landscapes, such as those on Mars.