This paper presents a method for estimating the six-degrees-of-freedom transformation between a camera and the body of the robot on which it is rigidly attached. The robot maneuvers in front of a planar mirror, allowing the camera to observe fiducial features on the robot from several vantage points. Exploiting these measurements, we form a maximum-likelihood estimate of the camera-to-body transformation, without assuming prior knowledge of the robot motion or of the mirror configuration. Additionally, we estimate the mirror configuration with respect to the camera for each image. We validate the accuracy and correctness of our method with simulations and real-world experiments.