A relativistic electron-positron beam propagating through a magnetized electron-ion plasma is shown to generate both circularly and linearly polarized synchrotron radiation. The degrees of circular and linear polarizations depend both on the density ratio of pair beam to background plasma and initial magnetization, and a maximum degree of circular polarization $langle P_textrm{circ}rangle approx 18%$ is found to occur for a tenuous pair beam. We demonstrate that the generation of circularly polarized radiation is intrinsically linked to asymmetric energy dissipation of the pair beam during the filamentation instability dynamics in the electron-ion plasma. These results can help in understanding the recent observations of circularly polarized radiation from gamma-ray-bursts.
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