We present firstly equation of motion for the photon coupled to Weyl tensor in a Kerr black holespacetime and then study further the corresponding strong gravitational lensing.
We find that blackhole rotation makes propagation of the coupled photons more complicated, which brings about somenew features for physical quantities including the marginally circular photon orbit, the deflectionangle, the observational gravitational lensing variables and the time delay between two relativisticimages. There is a critical value of the coupling parameter for existence of the marginally circularphoton orbit outside the event horizon, which depends on the rotation parameter of black holeand the polarization direction of photons. As the value of coupling parameter is near the criticalvalue, we find that the marginally circular photon orbit for the retrograde photon increases with therotation parameter, which modifies a common feature of the marginally circular photon orbit in arotating black hole spacetime since it always decreases monotonously with the rotation parameterin 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 stronggravitational lensing as the photons couple to Weyl tensor.