Securing the Internet of Things (IoT) is a necessary milestone toward expediting the deployment of its applications and services. In particular, the functionality of the IoT devices is extremely dependent on the reliability of their message transmission. Cyber attacks such as data injection, eavesdropping, and man-in-the-middle threats present major security challenges. Securing IoT devices against such attacks requires accounting for their stringent computational power and need for low-latency operations. In this paper, a novel deep learning method is proposed to detect cyber attacks via dynamic watermarking of IoT signals. The proposed learning framework, based on a long short-term memory (LSTM) structure, enables the IoT devices to extract a set of stochastic features from their generated signal and dynamically watermark these features into the signal. This method enables the IoT's cloud center, which collects signals from the IoT devices, to effectively authenticate the reliability of the signals. Furthermore, the proposed method prevents complicated attack scenarios such as eavesdropping in which the cyber attacker collects the data from the IoT devices and aims to break the watermarking algorithm. Simulation results show that, with an attack detection delay of under 1 second, the messages can be transmitted from IoT devices with an almost 100% reliability.