The Digital Twin refers to a digital representation of any real-world counterpart allowing its management (from simple monitoring to autonomy). At the core of the concept lies the inclusion of the entire asset lifecycle. To enable all lifecycle parties to partake, the Digital Twin should provide a sharable data base. Thereby, integrity and confidentiality issues are pressing, turning security into a major requirement. However, given that the Digital Twin paradigm is still at an early stage, most works do not consider security yet. Distributed ledgers provide a novel technology for multi-party data sharing that emphasizes security features such as integrity. For this reason, we examine the applicability of distributed ledgers to secure Digital Twin data sharing. We contribute to current literature by identifying requirements for Digital Twin data sharing in order to overcome current infrastructural challenges. We furthermore propose a framework for secure Digital Twin data sharing based on Distributed Ledger Technology. A conclusive use case demonstrates requirements fulfillment and is followed by a critical discussion proposing avenues for future work.