The authors calculate the transient electric birefringence B(t) when an electric field is applied to polarizable, randomly branched polymers in a dilute solution. They find that it relaxes with time as a stretched exponential, B(t) approximately exp(-talpha). The exponent alpha is calculated both for a single mass N and for the very broad, percolation-like distribution of masses that is usually obtained when one synthesizes such polymers. In the former case, such experiments would show the difference between the statistics of lattice animals and that of swollen polymers. The latter case exhibits the influence of the mass distribution on the long time relaxation properties. The calculations are made both in the Zimm approximation for the hydrodynamics, and in the Rouse limit, where screening of the hydrodynamic interaction occurs at large distances for the stretched configurations.