Legged robots rely on an accurate calibration of the system's kinematics for reliable motion tracking of dynamic gaits and for precise foot placement when moving in rough terrain. In our automatic foot-eye calibration approach, a monocular camera is attached to the robot and observes the robot's moving feet, which are equipped with Augmented Reality (AR) markers. The measurements are used to formulate a non-linear least squares problem over a fixed time window in order to estimate the 33 unknown parameters. This is efficiently solved with the Levenberg-Marquardt algorithm and we get estimates for both the kinematic and the camera parameters. The approach is successfully evaluated on a real quadruped robot.