It is well known that electrically neutral excitons can still be affected by crossed electric and magnetic fields that make them move in a direction perpendicular to both fields. We show that a similar effect appears in the absence of external electric fields, in the case of scattering of an exciton flow by charged impurities in the presence of the external magnetic field. As a result, the exciton flow changes the direction of its propagation that may be described in terms of the Hall conductivity for excitons. We develop a theory of this effect, which we refer to as the anomalous exciton Hall effect, to distinguish it from the exciton Hall effect that arises due to the valley selective exciton transport in transition metal dichalcogenides. According to our estimations, the effect is relatively weak for optically active or bright excitons in conventional GaAs quantum wells, but it becomes significant for optically inactive or dark excitons, because of the difference of the lifetimes. This makes the proposed effect a convenient tool for spatial separation of dark and bright excitons.