In this work, we analyze the orientation of silver nanowires immersed in aqueous solutions, under the effect of alternating electric fields in a broad frequency range covering from a few Hz to several MHz. The degree of orientation is experimentally determined by electro-optical techniques, which present the advantage of measuring multiple particles at the same time. In the electro-orientation spectrum, we observe frequency dispersion in the kHz range and provide a theoretical explanation for this behavior: at high frequencies, charge separation in the nanoparticles leads to a large induced dipole responsible for strong orientation. On the other hand, at low frequencies, redistribution of the ions in solution gives rise to an induced double layer that screens the dipolar fields, and as a consequence, the degree of orientation decreases. Moreover, we measure the transient response when the electric field is switched off, from which the size distribution of the polydisperse sample is obtained. The results match those given by electron microscopy determinations.