In this paper, we investigate the problem of routing, rebalancing, and charging for autonomous electric mobility-on-demand systems with respect to traffic congestion. We analyze the problem at the macroscopical level and use a volume-delay function to capture traffic congestion. To solve this problem, we first formulate an optimization problem for routing and rebalancing. Then, we present heuristic algorithms to find the loop of the flow and examine the energy constraints within the resulting loop. We impose charging constraints on re-routing problem so that the new solution satisfies the energy constraint. Finally, we verify the effectiveness of our method through simulation.