Angle-of-arrival (AoA) estimation is a challenging problem for analog antenna arrays. Typical schemes use time-consuming beam scanning, and the resolution is limited to the scanning beam width. In this paper, we propose a virtual-subarray based AoA (ViSA) estimation scheme, which divides an analog array into two virtual subarrays and exploits phase difference between one pair of measurements for AoA estimation. The basic ViSA algorithm can obtain a direct AoA estimate from every two temporal measurements. We propose different subarray constructions which can lead to different accuracy of estimation. We provide closed-form expressions for the statistics of the estimation error. Based on the basic ViSA estimator, we develop two methods to combine multiple pairs of measurements, when they are obtained via sequential and multi-resolution scanning, respectively. Near-optimal estimators are derived for both methods, employing the maximum likelihood principle. Novel techniques are also proposed to address the typical phase ambiguity problem due to the periodic phase function. Simulation results demonstrate that the proposed scheme significantly outperforms existing ones.