Steering angle prediction is critical in the control of Autonomous Vehicles (AVs) and has attracted the attention of researchers, manufacturers, and insurance companies in the automotive industry. Different Deep Learning (DL) architectures have been applied to predict the steering angle of AVs in various scenarios. A survey on steering angle prediction based on deep learning algorithms can help expert researchers identify those areas that require development. Also, novice researchers can use the survey as a starting point. In this paper, we present a broad study on the recent advances made in DL architectures that covers the steering angle prediction of AVs. A new comprehensive taxonomy of the application of DL in steering angle prediction of AVs is created. The survey presents a concise research summary synthesis, and analysis. It is found that most researchers depend on Convolutional Neural Network (CNN) over other DL architectures in predicting the steering angle of autonomous driving vehicles. Also identified are open research problems. The prominent challenge facing DL-based steering angle prediction of AVs is lack of sufficient real-world datasets, which means that researchers largely depend on data generated from simulated environments. Lastly, alternative viewpoints to solve the identified open research challenges are proposed, pointing towards promising future research directions.