Ridesourcing fleets present an opportunity for rapid uptake of battery electric vehicles (BEVs) but adoption has largely been limited to small pilot projects. Lack of charging infrastructure presents a major barrier to scaling up, but little public information exists on the infrastructure needed to support ridesourcing electrification. With data on ridesourcing trips for New York City and San Francisco, and using agent-based simulations of BEV fleets, we show that given a sparse network of three to four 50 kW chargers per square mile, BEVs can provide the same level of service as internal combustion engine vehicles (ICEVs) at lower cost. This suggests that the cost of charging infrastructure is not a significant barrier to ridesourcing electrification. With coordinated use of charging infrastructure across vehicles, we also find that fleet performance becomes robust to variation in battery range and placement of chargers. Our analysis suggests that mandates on ridesourcing such as the California Clean Miles Standard could achieve electrification without significantly increasing the cost of ridesourcing services.