We investigate the upper-crustal structure of the Rukwa-Tanganyika Rift Zone, East Africa, where earthquakes anomalously cluster at the northwestern tip of the Rukwa Rift, the eastern tip of the Mweru-Wantipa Rift, and along the Tanganyika Rift axis. The current rift tips host distributed faulting in exposed basement with little sedimentation. Here, we invert earthquake P and S travel times for three-dimensional upper-crustal velocity models for the region. The highest Vp/Vs ratios occur at the Rukwa and Mweru-Wantipa rift tips, and near a paleo-rift tip along an exhumed intra-basement shear zone beneath the Rukwa Rift. Colocated distributed faulting, upper-crustal seismicity, and thermal anomalies with high Vp/Vs ratios suggest a weakened crust at the rift tips. We propose an ongoing strain localization and crustal softening at the rift tips, accommodated by brittle damage and hydrothermal weakening of the crust, potentially representing a precursory phase that may initiate unilateral rift tip propagation.