Traffic routing is vital for the proper functioning of the Internet. As users and network traffic increase, researchers try to develop adaptive and intelligent routing algorithms that can fulfill various QoS requirements. Reinforcement Learning (RL) based routing algorithms have shown better performance than traditional approaches. We developed a QoS-aware, reusable RL routing algorithm, RLSR-Routing over SDN. During the learning process, our algorithm ensures loop-free path exploration. While finding the path for one traffic demand (a source destination pair with certain amount of traffic), RLSR-Routing learns the overall network QoS status, which can be used to speed up algorithm convergence when finding the path for other traffic demands. By adapting Segment Routing, our algorithm can achieve flow-based, source packet routing, and reduce communications required between SDN controller and network plane. Our algorithm shows better performance in terms of load balancing than the traditional approaches. It also has faster convergence than the non-reusable RL approach when finding paths for multiple traffic demands.