This paper investigates the problem of classification of unmanned aerial vehicles (UAVs) from radio frequency (RF) fingerprints at the low signal-to-noise ratio (SNR) regime. We use convolutional neural networks (CNNs) trained with both RF time-series images and the spectrograms of 15 different off-the-shelf drone controller RF signals. When using time-series signal images, the CNN extracts features from the signal transient and envelope. As the SNR decreases, this approach fails dramatically because the information in the transient is lost in the noise, and the envelope is distorted heavily. In contrast to time-series representation of the RF signals, with spectrograms, it is possible to focus only on the desired frequency interval, i.e., 2.4 GHz ISM band, and filter out any other signal component outside of this band. These advantages provide a notable performance improvement over the time-series signals-based methods. To further increase the classification accuracy of the spectrogram-based CNN, we denoise the spectrogram images by truncating them to a limited spectral density interval. Creating a single model using spectrogram images of noisy signals and tuning the CNN model parameters, we achieve a classification accuracy varying from 92% to 100% for an SNR range from -10 dB to 30 dB, which significantly outperforms the existing approaches to our best knowledge.