The transient electric birefringence (TEB) of polyelectrolytes reflects not only the rotational motion of the macroions but also the dynamics of the surrounding ion atmosphere. A rigorous formulation of the coupled rotational and ion atmosphere dynamics of a rod-like macroion with no permanent dipole moment is presented under the assumptions that (1) distortions of the ion atmosphere along the long axis of the molecule are the only source of induced dipole moments and (2) the dynamics of the ion atmosphere can be described by a single relaxation time. A coupled diffusion equation for the joint probability that the macroion has a certain orientation and a certain instantaneous dipole moment is derived and solved in the low field limit. In this way, simple analytic expressions for the TEB are obtained when the electric field is (1) turned on, (2) reversed, and (3) oscillates sinusoidally. These expressions reduce to the classical permanent dipole results when the ion atmosphere relaxation is slow and to the instantaneously induced dipole (polarizable) results when the relaxation is rapid compared to rotation. An illustrative application to the analysis of experimental TEB data on a short DNA restriction fragment is presented and various extensions of the theory are discussed.