The continuous increase in the number of mobile and Internet of Things (IoT) devices, as well as in the wireless data traffic they generate, represents an essential challenge in terms of spectral coexistence. As a result, these devices are now expected to make efficient and dynamic use of the spectrum by employing Cognitive Radio (CR) techniques. In this work, we focus on the Automatic Modulation Classification (AMC). AMC is essential to carry out multiple CR techniques, such as dynamic spectrum access, link adaptation and interference detection, aimed at improving communications throughput and reliability and, in turn, spectral efficiency. In recent years, multiple Deep Learning (DL) techniques have been proposed to address the AMC problem. These DL techniques have demonstrated better generalization, scalability and robustness capabilities compared to previous solutions. However, most of these techniques require high processing and storage capabilities that limit their applicability to energy-and computation-constrained end-devices. In this work, we propose a new gated recurrent unit neural network solution for AMC that has been specifically designed for resource-constrained IoT devices. We trained and tested our solution with over-the-air measurements of real radio signals. Our results show that the proposed solution has a memory footprint of 73.5 kBytes, 51.74% less than the reference model, and achieves a classification accuracy of 92.4%.