In polar semiconductors and oxides, the long-range nature of the electron-phonon interaction is a bottleneck to compute charge transport from first principles. Here, we develop an efficient ab initio scheme to compute and converge the relaxation times (RTs) and electron mobility in polar materials. We apply our approach to GaAs, where by using the Boltzmann equation with state-dependent RTs, we compute mobilities in excellent agreement with experiment at . The RTs and the phonon contributions to intravalley and intervalley scattering are also analyzed. Our work enables efficient ab initio computations of transport and carrier dynamics in polar materials.