The composition of the relativistic plasma produced in active galactic nuclei and ejected via powerful jets into the interstellar/intergalactic medium is still a major unsettled issue. It might be a positron-electron plasma in case the plasma was created by pair production in the intense photon fields near accreting super-massive black holes. Alternatively, it might be an electron-proton plasma in case magnetic fields lift and accelerate the thermal gas of accretion discs into relativistic jets as the recent detection of $gamma$-rays from blazars indicates. Despite various attempts to unambiguously establish the composition of the relativistic jets, this remains a major unknown. Here, we propose a way to settle the question via sensitive measurements of circular polarization (CP) in the radio emission of the hot spots of bright radio galaxies like Cygnus A. The CP of synchrotron emission is determined by the circular motions of the radiating relativistic leptons. In case of charge symmetric energy spectra of a electron-positron plasma, it should be exactly zero. In case of an electron-proton plasma the electrons imprint their gyration onto the CP and we expect the hot spots of Cygnus A to exhibit a fractional CP at a level of $10^{-3},( u/mbox{GHz})^{-{1}/{2}}$, which is challenging to measure, but not completely unfeasible.