  We present firstly equation of motion for the photon coupled to Weyl tensor
in a Kerr black hole spacetime and then study further the corresponding strong
gravitational lensing. We find that black hole rotation makes propagation of
the coupled photons more complicated, which brings some new features for
physical quantities including the marginally circular photon orbit, the
deflection angle, the observational gravitational lensing variables and the
time delay between two relativistic images. There is a critical value of the
coupling parameter for existence of the marginally circular photon orbit
outside the event horizon, which depends on the rotation parameter of black
hole and the polarization direction of photons. As the value of coupling
parameter is near the critical value, we find that the marginally circular
photon orbit for the retrograde photon increases with the rotation parameter,
which modifies a common feature of the marginally circular photon orbit in a
rotating black hole spacetime since it always decreases monotonously with the
rotation parameter in the case without Weyl coupling. Combining with the
supermassive central object in our Galaxy, we estimated the observables
including time delays between the relativistic images in the strong
gravitational lensing as the photons couple to Weyl tensor.
