  We have investigated the motion for photons in the Kerr black hole spacetime
under the axion-photon coupling. The birefringence phenomena arising from the
axion-photon coupling can be negligible in the weak coupling approximation
because the leading-order contributions to the equations of motion come from
the square term of the coupling parameter. We find that the coupling parameter
makes the size of shadows slightly increase for arbitrary spin parameter. For
the rapid rotating black hole case with a larger coupling, we find that there
exist a pedicel-like structure appeared in the left of the D-type like
shadows.Comparing the shadow size of the Kerr black hole with the shadow size
of the Sgr A* and M87* black holes, we find that there is room for such a
theoretical model of the axion-photon coupling.
