Presented is a robust optimization strategy for the aerodynamic design of horizontal axis wind turbine rotors including the variability of the annual energy production due to the uncertainty of the blade geometry caused by manufacturing and assembly errors. The energy production of a rotor designed with the proposed robust optimization approach features lower sensitivity to stochastic geometry errors with respect to that of a rotor designed with the conventional deterministic optimization approach that ignores these errors. The geometry uncertainty is represented by normal distributions of the blade pitch angle, and the twist angle and chord of the airfoils. The aerodynamic module is a blade-element momentum theory code. Both Monte Carlo sampling and the univariate reduced quadrature technique, a novel deterministic uncertainty analysis method, are used for uncertainty propagation. The performance of the two approaches is assessed in terms of accuracy and computational speed. A two-stage multi-objective evolution-based optimization strategy is used. Results highlight that, for the considered turbine type, the sensitivity of the annual energy production to rotor geometry errors can be reduced by reducing the rotational speed and increasing the blade loading. The primary objective of the paper is to highlight how to incorporate an efficient and accurate uncertainty propagation strategy in wind turbine design. The formulation of the considered design problem does not include all the engineering constraints adopted in real turbine design, but the proposed probabilistic design strategy is fairly independent of the problem definition and can be easily extended to turbine design systems of any complexity.