We consider the nonlinear Klein-Gordon-Maxwell system derived from the Lagrangian integral(-1/4 F(mu nu)F(mu nu) + 1/2- nu(phi) - eA(mu)J(mu)(B)) on four-dimensional Minkowski space-time, where phi is a complex scalar field and F(mu nu) = partial derivative(mu)A(nu) - partial derivative(nu)A(mu) is the electromagnetic field. For appropriate nonlinear potentials nu, the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons introduced and studied by Lee and collaborators for pure complex scalar fields. In this article, we develop a rigorous dynamical perturbation theory for these solitons in the small e limit, where e is the electromagnetic coupling constant. The main theorems assert the long time stability of the solitons with respect to perturbation by an external electromagnetic field produced by the background current J(B), and compute their effective dynamics to O(e). The effective dynamical equation is the equation of motion for a relativistic particle acted on by the Lorentz force law familiar from classical electrodynamics. The theorems are valid in a scaling regime in which the external electromagnetic fields are O(1), but vary slowly over space-time scales of O(1/delta), and delta = e(1-k) for k is an element of (0, 1/2) as e ->0. We work entirely in the energy norm, and the approximation is controlled in this norm for times of O(1/e).