A dual-gripper robotic cell consists of multiple processing machines and one material handling robot, which can perform an unloading or a loading task one at a time but can hold two parts at the same time. We address a scheduling problem of the robotic cell that determines a robot task sequence when two part types are processed in a different set of machines and all machines have variable processing times within a given interval. The objective is to minimize the makespan. This study proposes a learning-based method, i.e., a reinforcement learning (RL) approach, for the first time, to address a dual-gripper robotic cell scheduling problem. The problem is modeled with a Petri net, a graphical and mathematical modeling tool, which is used as an environment in RL. The states, actions, and rewards are defined by using flow shop scheduling properties, features from a Petri net, and knowledge from previous studies of scheduling robotized tools. Then, the RL approach is compared to the first-in-first-out (FIFO) rule, which is generally used in practice, a swap sequence, which is widely used for cyclic scheduling of dual-gripper robotic cells, and a lower bound. The extensive experiments show that the proposed method performs better than FIFO and the swap sequence; moreover, the gap between the makespan of the proposed method and the lower bound is not large.