The low earth orbit (LEO) satellite constellation is regarded as an effective complement to the terrestrial communication system due to its seamless coverage and ultra-low latency. Unfortunately, the highly dynamic traffic volume, as well as the inherent nature of dynamic topology changes caused by frequent link handover and uncertain hardware failures, pose severe challenges in the design of reliable routing. However, most existing reliable routing approaches with distributed schemes only focus on information exchange between adjacent nodes, which makes them fail to perceive real-time global network changes and make optimal decisions. In this paper, we propose a software defined networking (SDN) based intelligent satellite routing (SISR) method to increase the adaptivity and reliability during the packet transmission process. With the facilitation of SDN, we manage the network in a hierarchical and centralized paradigm, and further implement a more refined form of reinforcement learning (RL) to enhance the fault-tolerant ability of satellite network routing. Experimental results show that our solution can reduce latency and packet loss ratio by more than 42% and 29% compared to baselines.