Cloud computing enables clients to acquire cloud resources dynamically and on demand for their cloud applications and services. For cloud providers, especially, Software as a Service (SaaS) providers, the prediction of future cloud resource requirements, such as CPU usage for their cloud applications, to implement client requests is a complex task because it depends on incoming workloads. Due to workload fluctuations, it is difficult for SaaS cloud providers to predict or forecast future demand for resource usage in the next time interval and, accordingly, to allocate the required resources. Furthermore, cloud computing systems consist of many virtual machines (VMs), which increases the complexity of the prediction problem due to the correlations that exist between the large workload data in these VMs. Therefore, accurate resource usage forecasting remains a challenge, and relatively few studies have explored the prediction of CPU usage for VMs in cloud data centers. This paper proposes an autonomic and intelligent workload forecasting method for cloud resource provisioning based on the concept of autonomic computing and a deep learning approach. In particular, to predict future demand for CPU usage and determine how to respond to workload fluctuations in the next interval, we propose an efficient deep learning model based on a diffusion convolutional recurrent neural network (DCRNN). Existing deep learning models that are widely applied cannot handle accurate real-time forecasting due to the presence of inconsistent and nonlinear workloads in cloud computing systems. The goal of the proposed deep learning model is to improve forecasting accuracy and minimize the error between the predicted and the actual workloads. The effectiveness of the proposed DCRNN-based deep learning model was evaluated using experiments on a real-world dataset of PlanetLab's CPU usage traces. The results indicate that the proposed approach outperformed other existing deep learning models, achieving a mean absolute percentage error of 0.18 and root-mean-square error of 2.40.