This paper presents a circularly polarized (CP) rectenna with the advantage of achieving high efficiency in both wide operating power and frequency ranges. The proposed rectenna is composed of a high-efficiency rectifier and broadband CP antenna. In the proposed rectifier, a novel wideband resistance compression technique is presented, highly improving the matching performance of the circuit in a wide range of input power and frequency. The technique is achieved by an impedance manipulation network and a coupled-lines-based resistance compression network (RCN). Theoretical analysis is carried out and closed-form equations are derived for the design of the rectifier. Simulated and measured results show that over 60% (up to 76%) conversion efficiency is achieved for the input power range of 5-17 dBm and frequency band of 1.7-2.9 GHz (mobile, Wi-Fi and ISM bands). Subsequently, unlike the conventional half-wavelength slot antenna, a compact CP antenna with a side length of quarter wavelength is designed by using a 1-wavelength loop slot and a coupled-line-based phase shifter. It has wide axial-ratio bandwidth and good radiation pattern. At last, by integrating the proposed rectifier together with the CP slot antenna, a broadband CP rectenna is completed with higher efficiency by about 18.6% than that without wideband RCN.