The paper presents a circularly polarized radial line slot array (CP RLSA) antenna with a nearly optimal monotonic variation of slot length with radius, in order to simultaneously reduce antenna side-lobe levels and to make the aperture phase distribution nearly uniform. It has additional advantages of excellent radiation efficiency, high gain and good overall bandwidth. The antenna comprises a single-layer radial transverse electromagnetic quasi-TEM waveguide with radiating slots on the aperture. The amplitude tapering is implemented by gradually varying slot lengths on the antenna aperture as a function of radial distance, utilizing a slot coupling analysis. Several antenna designs were investigated, each having a physical diameter of 345 mm (23λ0) and a thickness of 4.6 mm (0.3λ0), where λ0 is the free-space wavelength at the operating frequency of 20 GHz. A prototype was fabricated and measured, showing a good agreement between the predicted and measured results. The sidelobe levels at the operating frequency are less than-20 dB due to tapering in the near-field amplitude distribution. The measured magnitude of the input reflection coefficient (S11) of the antenna is below-10 dB within the frequency range of 19 GHz to 21 GHz. The antenna has a measured peak directivity and a peak gain of 34.3 dBic and 33.8 dBic, respectively. Both the measured 3dB directivity bandwidth and 3dB gain bandwidth are 5.4%. Aperture efficiency is 48% and radiation efficiency is 94.2% at the operating frequency. The fabricated antenna also successfully fulfilled the condition of circular polarization with an axial ratio bandwidth exceeding 5%.