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A linearly polarized radar antenna made by a slot array on the narrow wall of a rectangular waveguide has been widely used for shipborne applications. This paper proposes a circularly polarized waveguide narrow-wall slot array with a single layer dipole array mounted on it as a polarization converter. We can switch from linear polarization to circular polarization by mounting the dipole array in front of an existing linear polarization array. In a narrow-wall slot array, each slot has a different angle with respect to the waveguide axis to control the radiation power. This variation in the slot angle results in a large phase difference in the circularly polarized wave, when each dipole mounted on the inclined slot is designed to optimize the axial ratio of the element pattern and is making a constant angle with each slot. Grating lobes of -14 dB and -20 dB appear in the -35 dB Taylor distribution design of 1.2 m (47 elements) and 3.6 m (150 elements) in the 9.41 GHz band. The phase correction is realized by changing the angle between the slot and dipole though the axial ratio of the element in the boresight direction is degraded up to 4.0 dB in the worst case. The array pattern is still perfect circularly polarized. The level of the grating lobes after the phase control is about -18 dB and -26 dB for the circularly polarized antenna with 47 elements and 150 elements, respectively.