An extrinsic Fabry-Perot interferometer (EFPI) acoustic sensor based on a graphene membrane was proposed, combined with a cascade model of convolutional neural networks (CNN) and long short-term memory networks (LSTM), for the detection and identification of various types of small rotorcraft drones. Furthermore, a detailed analysis was conducted on the feature extraction, data acquisition device, and the number of sound source categories involved in the experimental process. Through experimental comparison, it was found that when the Mel frequency cepstral coefficient (MFCC) was used for feature extraction, the recognition effect was significantly better than that of the short-time Fourier transform (STFT) and Mel spectrogram features. Moreover, the accuracy rate of using this sensor for small rotary-wing drones detection and recognition is approximately 2% higher than that of an electrical microphone. In addition, the recognition accuracy of the sound sources of various types of small rotary-wing drones is above 95.33%, which proves that it can effectively detect and identify multiple types of drones.