The OGY method is one of control methods for a chaotic system. In the method, we have to calculate a target periodic orbit embedded in its chaotic attractor. Thus, we cannot use this method in the case where a precise mathematical model of the chaotic system cannot be identified. In this case, the delayed feedback control proposed by Pyragas is useful. However, even in the delayed feedback control, we need the mathematical model to determine a feedback gain that stabilizes the periodic orbit. Thus, we propose a reinforcement learning algorithm to the design of a controller for the chaotic system. Recently, reinforcement learning algorithms with deep neural networks have been paid much attention to. Those algorithms make it possible to control complex systems. We propose a controller design method consisting of two steps, where we determine a region including a target periodic point first, and make the controller learn an optimal control policy for its stabilization. The controller efficiently explores its control policy only in the region.