Magnetic skyrmions can be driven by an applied spin-polarized electron current that exerts a spin-transfer torque on the localized spins constituting the skyrmion. However, the longitudinal dynamics is plagued by the skyrmion Hall effect, which causes the skyrmions to acquire a transverse velocity component. We show how to use spin-orbit interaction to control the skyrmion Hall angle and how the interplay of spin-transfer and spin-orbit torques can lead to a complete suppression of the transverse motion. Since the spin-orbit torques can be controlled all electronically by a gate voltage, the skyrmion motion can be steered all electronically on a broad racetrack at high speed and conceptually new writing and gating operations can be realized.