Based on a pay-as-you-go model, cloud computing provides the possibility of hosting pervasive applications from both academic and business domains. However, data centers hosting cloud applications consume huge amounts of electrical energy, contributing to high operational costs and large carbon footprints to the environment. Energy-aware resource provisioning is an effective solution to diminish the energy consumption of cloud data centers. Recently, a growing trend has emerged, where cloud technology is used to run periodic real-time applications such as multimedia, telecommunication, video gaming, and industrial applications. In order for a real-time application to be able to use cloud services, cloud providers have to be able to provide timing guarantees. In this paper, we introduce an energy-aware resource provisioning mechanism for cloud data centers, which are capable of serving real-time periodic tasks following the Software as a Service model. The proposed method is compared against an energy-aware version of the RT-OpenStack. RT-OpenStack is a recently proposed approach to provide a time-predictable version of OpenStack. The experimental results manifest that our proposed resource provisioning method outperforms energy-aware version of the RT-OpenStack by 16.01%, 25.45%, and 25.45% in terms of energy consumption, number of used servers, and average utilization of used servers, respectively. Moreover, from the scalability perspective, the preference of the proposed method for large-scale data centers is more considerable.