The rotational diffusion of electrically polarized metal nanowires suspended in an electrolyte is studied. The alignment of a Brownian nanowire in an ac field with a given direction is not complete due to thermal (fluctuating) torques. The orientation distribution allows us to examine the electrokinetic torques acting on the nanowire for smaller voltages than in previous deterministic experiments. In addition, the torques are obtained without recurring to the rotational friction coefficient as in dynamic deterministic experiments. The present results are in accordance with previous deterministic results of electro-orientation of metal nanowires. Nanowire rotation is originated by both the electrical torque on the induced dipole and by induced-charge electro-osmotic flow around the particle. At low frequencies of the applied ac field, induced-charge electro-osmotic orientation dominates while induced dipole torque orientation dominates at high frequencies. The angular standard deviation and the rotational rate are calculated from the measured fluctuating angle as a function of time, and good agreement with theoretical predictions is found. The experiments at high frequency indicate that the electrical torque on a nanowire near an insulating wall is reduced with respect to the bulk.