In this paper, we proposed a novel dual-band circularly polarized rectifier antenna for collecting environmental electromagnetic energy at 2.4 and 5.8 GHz. The receiving antenna is a circularly polarized microstrip slot antenna that achieves circular polarization in the low-frequency band (2.4 GHz) and high-frequency band (5.8 GHz) through the use of the “U” slot of the ground and the “L” branch of the upper patch, respectively. The antenna exhibits impedance bandwidths of 320 MHz (2.18–2.50 GHz) and 3.73 GHz (5.33–9.06 GHz) in the 2.4 GHz and 5.8 GHz bands, respectively, while the 3 dB axis specific bandwidths are 260 MHz (2.32–2.58 GHz) and 420 MHz (5.66–6.08 GHz), respectively. The antenna gains are 3.5 dBi and 6.2 dBi at 2.4 GHz and 5.8 GHz, respectively. Furthermore, a dual-frequency voltage doubling rectifier circuit was designed to operate with the antenna. A dual-branch matching circuit was used to achieve impedance matching between the antenna and the rectifier circuit, and the output was optimized to suppress high-order harmonics through sector branches to improve the rectification efficiency. The simulation results show that the maximum rectification efficiency of the circuit is more than 80%, with a measured efficiency of over 60%. This 2.4–5.8 GHz dual-band circularly polarized rectifier antenna has the potential to self-power low-power devices in the Internet of Things, making it a valuable contribution to the field of wireless energy harvesting.