The curvature radiation is applied to the explanation of the circular polarization of fast radio bursts (FRBs). Significant circular polarization is reported in both apparently non-repeating and repeating FRBs. Curvature radiation can produce significant circular polarization at the wing of the radiation beam. In the curvature radiation scenario, in order to see significant circular polarization in FRBs, (1) more energetic bursts, (2) bursts with electrons having higher Lorentz factor, and (3) a slowly rotating neutron star at the center are required. Different rotational period of the central neutron star may explain why some FRBs have high circular polarization, while others do not. Considering possible difference in refractive index for the parallel and perpendicular components of electric field, the position angle may change rapidly over the narrow pulse window of the radiation beam. The position angle swing in FRBs may also be explained by this non-geometric origin, besides that of the rotating vector model.

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