Creatures as varied as mammals, fish, insects, reptiles, and birds have an intriguing sixth sense that allows them to orient themselves in the Earth's magnetic field. Despite decades of study, the physical basis of this magnetic sense remains elusive. A likely mechanism is furnished by magnetically sensitive radical pair reactions occurring in the retina, the light-sensitive part of animal eyes. A photoreceptor, cryptochrome, has been suggested to endow birds with magnetoreceptive abilities as the protein has been shown to exhibit the biophysical properties required for an animal magnetoreceptor to operate properly. Here, we propose a theoretical analysis method for identifying cryptochrome's signaling reactions involving comparison of measured and calculated reaction kinetics in cryptochrome. Application of the method yields an exemplary light-driven reaction cycle, supported through transient absorption and electron-spin-resonance observations together with known facts on avian magnetoreception. The reaction cycle permits one to predict magnetic field effects on cryptochrome activation and deactivation. The suggested analysis method gives insight into structural and dynamic design features required for optimal detection of the geomagnetic field by cryptochrome and suggests further experimental and theoretical studies.