  In this work, we calculate the quantum correction effects on the deflection
of light in the spacetime geometry of a quantum improved Kerr black hole
pierced by an infinitely long cosmic string. More precisely, we calculate the
deflection angle by applying the Gauss--Bonnet theorem (GBT) to the osculating
optical geometries related to the quantum improved rotating black hole in the
weak limit approximation. We find that the deflection angle of light is
affected by the quantum effects as well as the global topology due to the
presence of the cosmic string. Besides, we have managed to find the same
expression for the deflection angle in leading order terms using the geodesic
equations.
