**Published: **

In this letter we apply the Gauss--Bonnet theorem 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 Gauss--Bonnet theorem and calculate the Gaussian curvature in both cases. Finally, we calculate the leading terms of the deflection angle and show that quantum corrections modifies the deflection angle in both solutions.