This paper introduces a new analytical method suitable for the design of the single-feed circular polarization (CP) microstrip patch antenna. Specifically, the proposed method imposes simultaneously the circular polarization condition as well as an arbitrary input impedance matching condition. The two conditions are enforced by an analytical method derived from an equivalent circuit model of a quasi-symmetrical patch antenna, and manipulated to control the modal detuning. This method can be used as an aid to speed up the design procedure for CP antennas even working with a numeric CAD tool. The validation of this approach is proven designing and fabricating a prototype implementing an original design, which consists of a circular disc slotted by a concentric elliptical cut with coaxial feed and operating at the center frequency of 2.45 GHz. The fabricated prototype exhibited a return loss of about 19 dB, within an impedance bandwidth of 130 MHz, a measured gain of 3.85 dB and a 0 dB axial ratio at 2.45 GHz with a corresponding modal phase difference of 87 degrees.