We present an approach that uses Reinforcement Learning (RL) with the Random Neural Network (RNN) acting as an adaptive critic, to route traffic in a SDN network, so as to minimize a composite Goal function that includes both packet delay and energy consumption per packet. We directly measure the traffic dependent energy consumption characeristics of the hardware that we use (including energy expended per packet) so as to parametrize the Goal function. The RL based algorithm with the RNN is implemented in a SDN controller that manages a multi-hop network which assigns service requests to specific servers so as to minimize the desired Goal. The overall system’s performance is evaluated through experimental measurements of packet delay and energy consumption under different traffic load values, demonstrating the effectiveness of the proposed approach.