The study of impulsive astrophysical radio emission makes it possible to probe the intervening plasma between the emission source and the Earth. In cold electron-ion plasmas, the circular propagating wave modes primarily alter the linear polarization plane that scales with the inversesquare of the emission frequency. In relativistic plasmas, the wave modes are elliptically polarized, and it is possible to convert linearly polarized emission into circular and vice versa. Fast radio bursts (FRBs) enable the study of not only the electron-ion plasma of the intergalactic medium but potentially the extreme magneto-ionic medium in which these intense pulses are produced.Here we report on the polarimetric analysis of a repeat burst from the FRB 20201124A source. The burst displayed a significant frequency-dependent circularly polarized component, unlike other bursts from this source or any other FRB found to date. We model the frequency dependence of the circular polarization using a phenomenological generalized Faraday rotation framework. From this, we interpret the observed circular polarization in the burst as having been induced by radiative propagation through a relativistic plasma within or close to the magnetosphere of the progenitor.