The kinematics of rift segment linkage in magmatic rifts remain debated. Strain patterns from Afar provide tests of current models of how segmented rifts grow in areas of incipient oceanic spreading. Here, we present a combined analysis of seismicity, interferometric synthetic aperture radar (InSAR), and GPS–derived strain rate maps to reveal that the plate-boundary linkage between the Red Sea and Gulf of Aden rifts of Afar is accommodated primarily by distributed extensional faulting. Large rotations about vertical axes predicted by bookshelf faulting models are not detected. Additionally, models of stress changes and seismicity induced by recent dikes provide poor fits to the observed time-space patterns of strike-slip earthquakes. Instead, we explain these features as resulting from rift-perpendicular shearing at the tips of spreading rifts where extension terminates against less stretched lithosphere. Our results demonstrate that distributed extension drives rift-perpendicular shearing, achieving plate-boundary linkage during incipient seafloor spreading.