The magnetic compass sense of migratory songbirds is thought to derive from magnetically sensitive photochemical reactions in cryptochromes located in photoreceptor cells in the birds’ retinas. More specifically, transient radical pairs formed by light-activation of these proteins have been proposed to account for the birds’ ability to orient themselves using the Earth’s magnetic field and for the observation that radiofrequency magnetic fields, superimposed on the Earth’s magnetic field, can disrupt this ability. Here, by means of spin dynamics simulations, we show that it may be possible for the birds to orient in a monochromatic radiofrequency field in the absence of the Earth’s magnetic field. If such a behavioural test were successful, it would provide powerful additional evidence for a radical pair mechanism of avian magnetoreception.