The rapid development of Internet of Things (IoT) enables digital twin (DT) technology to precisely represent a real product in a virtual space by generating a multitude of IoT data items to record many aspects of the product. To support various DT-based applications, the generated IoT data items need to be shared among multiple parties involving the lifecycle of the product, which raises increasing demand for data access control. The decentralization and tamper-proofing properties of blockchain enable it a promising technology to support immutability protection of shared IoT data items. Meanwhile, to protect the confidentiality of the shared IoT data items, attribute-based encryption (ABE) can be used as a common tool to construct a cryptographic enforced data access control scheme. However, its adoption has been severely hindered by the incompatibility between the immutability of blockchain and secure authority update of cryptographic enforced data access control. In this paper, a blockchain-aware rollbackable data access control scheme (Bdacs) is proposed to reconcile the above tension. Bdacs uses two novel encryption schemes named hierarchical encryption scheme and privacy-preserving rollback re-encryption scheme to realize secure dynamic access control while preserving the immutability of blockchain. We prove the security of Bdacs and evaluate it through theoretical comparison and experimental analysis to confirm its efficiency. This work can serve as a basis of development of future DT-based applications to enable privacy-preserving IoT data-sharing systems deployed on blockchain.