Drone detection and classification, important in military and civilian applications, are performed using different sensor signals. Proposed study handles this task using Radio Frequency (RF) signals utilizing basic machine learning methods. It is composed of two main stages as feature extraction succeeded by training/testing of the model. In feature extraction stage, valuable information for classification, contained in the RF signal, is obtained. For this purpose, spectral features, frequently used in speech processing applications, are employed. Specifically, Power Spectral Density (PSD), Mel-Frequency Cepstral Coefficients (MFCC) and Linear Frequency Cepstral Coefficients (LFCC) are adopted by adjusting filter bank margins and parameters for this task. In the second stage, a Support Vector Machine (SVM) classifier is first trained based on the obtained features and finally tested to measure its performance. All experimental studies are carried out using publicly available DroneRF dataset. This dataset contains 2-Class, 4-Class and 10-Class samples for drone existence vs. background (BG), drone types and drone operation modes, respectively. The best classification results are obtained using, PSD, MFCC and LFCC based features for 2-Class, MFCC and LFCC based features for 4-Class and LFCC based features for 10-Class. Accuracy rates for 2-Class, 4-Class and 10-Class are 100%, 98.67% and 95.15%, respectively. These results show that the proposed method outperforms the results given in the literature for DroneRF dataset.