We study the broadband polarization of hydrogen lines produced by scattering of radiation, in the presence of isotropic electric fields. In this paper, we focus on two distinct problems: (a) the possibility of detecting the presence of turbulent electric fields by polarimetric methods and (b) the influence of such fields on the polarization due to a macroscopic, deterministic magnetic field. We found that isotropic electric fields decrease the degree of linear polarization in the scattered radiation, with respect to the zero-field case. On the other hand, a distribution of isotropic electric fields superimposed onto a deterministic magnetic field can increase significantly the degree of magnetic-induced, net circular polarization. This phenomenon has important implications for the diagnostics of magnetic fields in plasmas using hydrogen lines, because of the ubiquitous presence of the Holtsmark microscopic electric field from neighbouring ions. In particular, previous solar magnetographic studies of the Balmer lines of hydrogen may need to be revised because they neglected the effect of turbulent electric fields on the polarization signals. In this work, we give explicit results for the Lyman α and Balmer α lines.