With the vision of 6G networks, the Radio Access Networks (RAN) are expected to entail increased programmability, efficiency, and flexibility. The current trends in Open RAN architecture that promote openness, disaggregation, and inherent intelligence are well aligned with these aspects. The Open RAN architecture's highly dynamic nature and the datadriven approaches necessitate more cognitive and proactive security measures with robust defensive mechanisms. Digital Twin (DT) is proven to be an ideal platform to integrate into such dynamic systems for testing and optimizing configurations and security algorithms. In this paper, we propose a DT-based security framework for Open RAN (O-RAN) with an elaboration of a use case of security service level agreement (SSLA) assurance management. Moreover, we describe how to integrate energyaware solutions, such as green security policies, within the proposed framework.