Fast radio bursts (FRBs) are extra-galactic sources with unknown physical mechanisms. They emit millisecond-duration radio pulses with isotropic equivalent energy of $10<^>{36}$-$10<^>{41}$ ergs. This corresponds to a brightness temperature of FRB emission typically reaching the level of $10<^>{36}$ K, but can be as high as above $10<^>{40}$ K for sub-microsecond timescale structures, suggesting the presence of underlying coherent relativistic radiation mechanisms. Polarization carries key information to understand the physical origin of FRBs, with linear polarization usually tracing the geometric configuration of magnetic fields and circular polarization probing both intrinsic radiation mechanisms and propagation effects. Here we show that the repeating source FRB 20201124A emits $90.9\%\pm 1.1\%$ circularly polarized radio pulses. Such a high degree of circular polarization was unexpected in theory and unprecedented in observation in the case of FRBs, since such a high degree of circular polarization was only common among solar or Jovian radio activities, attributed to the sub-relativistic electrons. We note that there is no obvious correlation between the degree of circular polarization and burst fluence. Besides the high degree of circular polarization, we also detected a rapid swing and orthogonal jump in the position angle of linear polarization. The detection of high-degree circular polarization in FRB 20201124A, together with its linear polarization properties that show orthogonal modes, place strong constraints on FRB physical mechanisms, calling for an interplay between magnetospheric radiation and propagation effects in shaping the observed FRB radiation. The largest radio telescope FAST detects 90% circular polarization and rapidly changing linear polarization in the bursts of a fast radio burst (FRB) repeater, imposing new constraint on radiative mechanism of FRBs.