This paper presents an RF energy harvesting system for polarization independence and stability of the time-varying signal. The harvesting system has an antenna, a rectifier, and a power management unit (PMU). A multi-port antenna is designed for ambient RF energy harvesting. Rectifiers are connected to the multi-port antenna to be polarization-independent. The PMU is connected to the output of the rectifier for stable operation, eliminating discontinuities in energy harvesting. In this paper, a harvesting system is designed by the proposed scheme. The stability and polarization independence of the proposed Ambient RF energy harvesting system is verified by experiments.