Radio orbital angular momentum (OAM) communications require accurate alignment between the transmit and receive beam directions. Accordingly, a key feature of OAM receivers is the ability to reliably estimate the angle of arrival (AoA) of multi-mode OAM beams. Considering the limitations of existing AoA estimation techniques, in this paper, we propose an easier-to-implement AoA estimation method based on applying multiple times the estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm to the received training signals in OAM mode and frequency domains, which is denoted as the mode-frequency (M-F) multi-time (MT)-ESPRIT algorithm. With this method, the misalignment error of real OAM channels can be greatly reduced and the performance approaches that of ideally aligned OAM channels.