Adaptive control strategies are commonly used for systems that change over time, such as wind turbines. Extremum Seeking Control (ESC) is a model-free real-time adaptive control strategy commonly used in conventional gearbox wind turbines for Maximum Power Point Tracking (MPPT). ESC optimizes the rotor power by constantly tuning the torque control gain (k) when operating below rated power. The same concept can be applied for hydrostatic wind turbines. This paper studies the use of ESC for a 60-kW hydrostatic wind turbine. First, a systematic approach to establish the ideal ESC is shown. Second, a comparison of the power capture performance of ESC versus the conventional torque control law (the kω2 law) is shown. The simulations include a timesharing power capture coefficient (Cp) to clearly show the advantages of using ESC. Studies under steady and realistic wind conditions show the main advantages of using ESC for a hydrostatic wind turbine.