Carsharing has received increased attention from the Operations Research community in recent years. Currently, many systems are adopting electric vehicles that require charging when battery levels fall below a given level. To do this, staff is often used to move cars to charging stations. Repositioning cars, rather than simply moving them to the closest charging station, might provide a better distribution of cars and in turn generate increased revenue and customer service while only marginally increase the operational costs. We present a mathematical model for the problem of charging and repositioning a fleet of shared electric cars. The model considers the assignment of cars to charging stations and the routing of staff and service vehicles. The complexity of the resulting mixed integer program makes it impossible to solve real world instances using a commercial solver. Therefore, we propose a new Hybrid Genetic Search with Adaptive Diversity Control algorithm. Tests based on data from a real life carsharing organization demonstrate that the proposed method can handle real size instances and that combining repositioning and charging operations can give significant benefits.