The electrification of road transport, as the predominant mode of transportation in Africa, represents a great opportunity to reduce greenhouse gas emissions and dependence on costly fuel imports. However, it introduces major challenges for local energy infrastructures, including the deployment of charging stations and the impact on fragile electricity grids. Existing planning tools often depend on detailed mobility data that is unavailable in many African contexts, especially for privately owned passenger vehicles. To address this gap, we introduce a novel and open framework designed to support the electrification of private vehicles in data-scarce regions. We apply our approach to a case study of Addis Ababa, where we model the introduction of 100,000 electric vehicles, simulating their daily mobility patterns and charging needs. Our analysis estimates a daily charging demand of approximately 350 MWh and underscores the importance of the charging location on the spatial and temporal distribution of this demand. Notably, charging at public places can help smooth the charging demand throughout the day, mitigating peak charging loads on the electricity grid. We also estimate charging station requirements, finding that workplace charging requires approximately one charging point per three electric vehicles, while public charging requires only one per thirty. Finally, we demonstrate that photovoltaic energy can cover a substantial share of the charging needs, emphasizing the potential for renewable energy integration. Demonstrated through its application in Addis Ababa, this study provides a transferable framework for electric vehicle planning in other data-scarce cities.