This paper discusses a means of enhancing the accuracy of the direction of arrival (DoA) estimates of backscattered signals from passive ultra high frequency radio frequency identification (UHF RFID) tags. The DoA estimation is carried out by using the root-MUSIC algorithm on a two-element receive antenna array, which is realized through a RFID reader configuration involving a mono-static (Tx/Rx) antenna and an additional receive-only antenna. We show that accurate DoA estimation of RFID tag signals is hampered by inherent self-interference in such RFID systems, which is caused by the high power transmission of the reader leaking into the receiver through imperfect isolation. The proposed enhancement involves utilizing a Least Mean Square (LMS) adaptive filter to successfully suppress the carrier leakage prior to DoA estimation. Simulation results show substantial reduction in the standard deviation of error of the estimated DoA.