This article presents a novel, compact, and flexible dual-band magnetoelectric dipole rectenna designed for radio frequency (RF) energy harvesting. The rectenna consists of a unique antenna structure, combining electric and magnetic dipoles to create unidirectional radiation patterns, minimizing interference from the human body. The rectifier is integrated with the antenna through conjugate matching, eliminating the need for additional matching circuits, reducing circuit losses, minimizing design complexity, and improving conversion efficiency. The proposed rectenna utilizes a flexible graphene film as the radiating element, which offers excellent conductivity and corrosion resistance, enabling conformal operation in diverse scenarios. Simulation and experimental results show that the rectenna operates effectively at 3.5 GHz and 4.9 GHz, achieving peak conversion efficiencies of 53.43% and 43.95%, respectively, at an input power of 4 dBm. The simulated and measured results achieved good agreement. The rectenna maintains stable performance under various bending conditions, demonstrating its suitability for flexible, wearable RF energy-harvesting systems.