A formalism is given which makes it possible for a modified form of local gauge invariance and minimal coupling to be compatible with torsion. One consequence is a restriction on the possible form of torsion in that it must be determined by the gradient of a scalar function. Furthermore, a dynamical theory is obtained for this scalar and hence allows propagation of torsion in vacuum. The Lagrangian density for interacting electromagnetic, gravitational, torsion, and complex scalar fields is presented, as well as the resulting field equations. The formalism implies the existence of both electric and magnetic currents due to the interaction of the electromagnetic and torsion fields.