Calibrating the absolute energy scale of air showers initiated by ultrahigh energy (UHE) cosmic rays is an important experimental issue. Currently, the corresponding systematic uncertainty amounts to 14%-21% using the fluorescence technique. Here, we describe a new, independent method which can be applied if ultrahigh energy photons are observed. While such photon-initiated showers have not yet been identified, the capabilities of present and future cosmic-ray detectors may allow their discovery. The method makes use of the geomagnetic conversion of UHE photons (preshower effect), which significantly affects the subsequent longitudinal shower development. The conversion probability depends on photon energy and can be calculated accurately by QED. The comparison of the observed fraction of converted photon events to the expected one allows the determination of the absolute energy scale of the observed photon air showers and, thus, an energy calibration of the air shower experiment. We provide details of the method and estimate the accuracy that can be reached as a function of the number of observed photon showers. Already a very small number of UHE photons may help to test and fix the absolute energy scale.