Range anxiety remains one of the key concerns for ride-sourcing drivers to adopt battery electric vehicles (BEVs). To investigate the feasibility of using BEVs for ride-sourcing services, we propose an optimization-based methodology to estimate the daily driving trip patterns of ride-sourcing vehicles based on widely available non-identifiable trip data. Furthermore, we investigate the charging needs of electrified ride-sourcing vehicles using agent-based simulation. The methodologies are illustrated through a case study in the city of Chicago. Through sensitivity analysis on driver working hours and initial charging status, we quantify the range of daily average vehicle miles traveled (VMT) per car and identify the hot spots of current public charging demand and potential unsatisfied charging demand. This study can be used to determine the priorities of future charging infrastructure investment to further mitigate range anxiety and promote adoption of electrified ride-sourcing services.