We consider current-driven motion of magnetic skyrmions in granular magnetic films. The study uses micromagnetic modeling and phenomenological analysis based on the Thiele formalism. Remarkably, the disorder enhances the effective skyrmion Hall effect that depends on the magnitude of the driving force (the cur- rent density and nonadiabaticity parameter). The origin is the sliding motion of the skyrmion along the grain boundaries, followed by pinning and depinning at the grain junctions. A side jump can occur during this depinning process. In addition, the critical current that triggers the skyrmion motion depends on the relative size of the crystallites with respect to the skyrmion size. Finally, when the skyrmion trajectory is confined along an edge by the nonadiabatic Magnus force, the critical current density can be significantly reduced. Our results imply that narrow nanowires exhibit higher skyrmion mobilities.