We use a rotating magnetic field to assemble an oblate cluster of paramagnetic colloidal particles. If the field is rotating about a horizontal axis, the cluster acts as a colloidal wheel rolling across the supporting glass surface. The motion is reversible upon switching the direction of rotation. Surprisingly, the reversibility is lost if the axis of field rotation is tilted with respect to the surface. The wheel then rolls in a direction that is not perpendicular to the field rotation axis. We explain the skewed rotation with an interplay between a magnetic driving torque, magnetic anisotropy and an anisotropy in the hydrodynamic mobility tensor in the vicinity of a surface. The opposing forward and backward drive induce opposite chirality in the degrees of freedom of the mechanically achiral colloidal wheel.