  In this letter we apply the Gauss--Bonnet theorem (GB) to calculate the
deflection angle by a quantum corrected Schwarzschild black hole in the weak
limit approximation. In particular we calculate the light deflection by two
types of quantum corrected black holes: the renormalization group improved
Schwarzschild solution and the quantum corrected Schwarzschild solution in
Bohmian quantum mechanics. We start from the corresponding optical metrics to
use then the GB theorem and calculate the Gaussian curvature in both cases. We
calculate the leading terms of the deflection angle and show that quantum
corrections modifies the deflection angle in both solutions. Finally by
performing geodesics calculations we show that GB method gives exact results in
leading order terms.
