The technique of driving steady Hall currents in plasmas using a transverse oscillating magnetic field is studied analytically under the approximation of negligible ion flow and in the weakly non-linear limit. The authors consider the situation of a uniform (transverse) oscillating field and a uniform vertical field applied to a spherical uniformly dense and resistive plasma with spherical insulating wall. They model the oscillating field as two counter-rotating fields; a transformation which allows the deduction of many of the properties of this form of current drive from the existing theory of current drive by rotating magnetic fields.