Airborne Wind Energy (AWE) is an emerging technology that promises to be able to harvest energy from strong high-altitude winds, while addressing some of the key critical issues of current wind turbines. AWE is based on flying devices (usually gliders or kites) that, tethered to a ground station, fly driven by the wind and convert the mechanical energy of wind into electrical energy by means of a generator.Such systems are usually controlled by adjusting the trajectory of the kite using optimal control techniques, such as model-predictive control. These methods are based upon a mathematical model of the system to control, and they produce results that are strongly dependent on the specific model at use and difficult to generalize. Our aim is to replace these classical techniques with an approach based on Reinforcement Learning (RL), which can be used even in absence of a known model. Experimental results prove that RL is a viable method to control AWE systems in complex simulated environments, including turbulent flows.