In this paper, we present a new single sound source DOA estimation and tracking system based on the well-known SRP-PHAT algorithm and a three-dimensional Convolutional Neural Network. It uses SRP-PHAT power maps as input features of a fully convolutional causal architecture that uses 3D convolutional layers to accurately perform the tracking of a sound source even in highly reverberant scenarios where most of the state of the art techniques fail. Unlike previous methods, since we do not use bidirectional recurrent layers and all our convolutional layers are causal in the time dimension, our system is feasible for real-time applications and it provides a new DOA estimation for each new SRP-PHAT map. To train the model, we introduce a new procedure to simulate random trajectories as they are needed during the training, equivalent to an infinite-size dataset with high flexibility to modify its acoustical conditions such as the reverberation time. We use both acoustical simulations on a large range of reverberation times and the actual recordings of the LOCATA dataset to prove the robustness of our system and its good performance even using low-resolution SRP-PHAT maps.