In this paper, a broadband left-handed circularly polarized (LHCP) corrugated horn antenna using a dielectric circular polarizer is proposed. Circularly polarized (CP) waves are generated by inserting an improved dovetail-shaped dielectric plate into the circular waveguide. Compared with the traditional dovetail-shaped circular polarizer, the proposed improved dovetail-shaped circular polarizer has a wider impedance bandwidth and 3 dB axial ratio bandwidth. A substrate-integrated waveguide (SIW) structure is designed as a wall to eliminate the influence of fixed grooves on the circular polarizer. The simulated reflection coefficient of the dielectric plate circular polarizer is less than −20 dB in the frequency band from 17.57 to 33.25 GHz. Then, a conical corrugated horn antenna with five corrugations and a four-level metal stepped rectangular-circular waveguide converter are designed and optimized. The simulated −10 dB impedance and 3 dB axial ratio (AR) bandwidths of the circularly polarized horn antenna integrated with the polarizer are 61% (17.1–32.8 GHz) and 60.9% (17.76–33.32 GHz), respectively. The simulated peak gain is 17.34 dBic. The measured −10 dB impedance is 52.7% (17.2–27.5 GHz).