This paper applies the computationally advantageous combination of a differential analysis technique and the adjoint method in the context of uncertainty quantification to the gradient-based robust design optimization of aerofoils. First, the accuracy and feasibility of the method is evaluated using an analytical test function. The method is subsequently applied to the robust design optimization of a rotor blade under geometric uncertainty, that is based on a parametrized population of optically 3D scanned blades. A significant improvement of the robustness w.r.t. the isentropic efficiency of the rotor is reported.