Virtual Reality (VR) applications have attracted great attention from both industry and academia in recent years. With an increasing demand for these applications, there is high pressure on resource and performance optimization using software-defined networking. In this paper, we consider one type of QoE models in the literature; and then use the Monte Carlo Tree Search and develop an SDN-based routing scheme to guarantee users' QoE for VR applications. Our routing scheme is tested using computer simulation in a $5\mathrm{x}5$ square grid network. Simulation results indicate that our routing scheme consistently outperforms the shortest path first (SPF) algorithm in terms of the QoE scores.