They do but it most likely doesn’t! There are experiments where the bird’s beaks had a local anesthesia applied and it had no effect on the bird’s sense of orientation. Instead it seems like it’s most likely something called cryptochrome in the eyes, where a quantum mechanism (radical pair reaction) might be taking place that could generate sense-able electrical signals. There is further evidence for this, like birds being unable to tell when a magnetic field is reversed 180° (which an iron-based compass should be able to), and their sense of direction being effectively turned off by mild RF interference at the right frequency, which also wouldn’t affect an iron compass.