Unmanned aerial vehicles (UAVs) are reported to be highly exposed as possible targets of cyber attacks, due to their strong strategic and economic value, and their increasing use in a wide range of operations. Among the most critical cyber attacks, replay attacks are performed by replacing the real data coming from the sensors with previously recorded data, causing deterioration of the control system's performance and potentially allowing other types of attacks without being discovered. The main contribution of this paper is to investigate the applicability of a frequency-based detection method, which uses a sinusoidal signal with a time-varying frequency as authentication signal, to a UAV affected by replay attacks. The effectiveness of the method is illustrated through simulation scenarios.