This paper builds a system for real-time tracking of a single target Radio Frequency (RF) signal source, in which the transmitter uses a low-cost HackRF One software radio transceiver platform, and the receiving antenna array uses two monopole antennas to form a 1×2 receiving array. The receiver uses Xilinx 7-Series development board Zedboard and AD9361 RF transceiver to build a wireless receiving platform to process the received signal. In this RF beam tracking system, it needs to perform Direction of Arrival (DOA) estimation on the calibrated signal, the DOA algorithm plays a crucial role in the accuracy of beam pointing and system running time, the MUSIC algorithm takes some time to conduct spectrum peak search, so the Root-Music algorithm is used here to avoid the spectrum peak search problem. To enable the Root-MUSIC algorithm to be better executed on this two-element receiving platform, this work simplifies the entire calculation process, requiring only a small amount of calculation and running time to complete the DOA estimation step, which effectively save FPGA processing time and computing resources. It provides a guarantee for the real-time performance of the system.