This paper presents a method to consider uncertainties in the distortion prediction of additive manufacturing processes within robust topology optimization. The random variable of the stochastic additive manufacturing process is the inherent thermomechanical strain, typically determined by process characterization experiments. The value of the inherent strain per se encompasses uncertainty due to differences between characterization and production geometries, uncontrolled process variations, hatching pattern choices, and other effects not captured in layer-by-layer part-scale additive manufacturing simulation. These effects can be represented by different inherent strains for each realized layer, therefore, model the variability in part distortion. Instead of employing a more detailed simulation approach, requiring significantly more process data and computation time, our method aims at generating a robust design in this setting, to obtain parts exhibiting reduced distortion regardless of uncertainties in distortion prediction. The formulation benefits from the superposition potential within the employed process simulation. For robust optimization, the expected part distortion and its estimated variance are included in the standard density-based topology optimization algorithm's objective function. The effectiveness of the approach is demonstrated by simultaneously optimizing structural performance combined with a minimized additive manufacturing part distortion under uncertain process conditions.