Securing low-power Internet-of- Things (IoT) sensor nodes presents a critical challenge for the widespread adoption of IoT technology, given their inherent limitations in energy, computation, and storage resources. As a promising alternative to conventional wireless security approaches based on cryptography, there has been a growing interest in RF physical-layer security, especially RF fingerprinting, which offers the promise of reduced overhead and energy consumption. In this work, we present an artificial neural network (ANN) model tailored to identify IoT transmitters by harnessing their unique power spectral density (PSD). The network is designed to be lightweight and can be readily implemented on resource-constrained IoT nodes. Combined with our customized radio frontend, we achieve superior identification performance. In the measurements, we can reliably identify 240 devices with a 99 % accuracy on trained distances and 40 devices with an above 95 % accuracy at an unknown distance that is excluded from the training data. These results demonstrate significant improvement in robustness, reliability, and identification accuracy over prior art while ensuring compatibility with resource-constrained IoT nodes.