Recent advances in small-scale unmanned aerial vehicles (UAVs) have opened up new horizons for establishing UAV-based free-space optical (FSO) links. However, FSO technology requires precise beam alignment while random fluctuations of hovering UAVs can induce beam misalignment and angle-of-arrival (AoA) fluctuations. For an FSO link to a UAV, we consider a quadrant detector array for optical beam tracking and study the effect of random hovering fluctuations of the UAV on the performance of the tracking method, and based on the degree of instabilities for the UAV, the optimum size of the detectors for minimizing the tracking error is found. Furthermore, for optimal detection of On - Off keying symbols, the receiver requires instantaneous channel fading coefficients. We propose a blind method to estimate the channel coefficients, i.e., without using any pilot symbols, to increase link bandwidth efficiency. To evaluate the performance of the considered system, closed-form expressions of tracking error and bit-error rate are derived. Moreover, Monte-Carlo simulation is carried out to corroborate the accuracy of the derived analytical expressions.