Privacy audit logs are used to capture the actions of participants in a data sharing environment in order for auditors to check compliance with privacy policies. However, collusion may occur between the auditors and participants to obfuscate actions that should be recorded in the audit logs. In this paper, we propose a Linked Data based method of utilizing blockchain technology to create tamper-proof audit logs that provide proof of log manipulation and non-repudiation. We also provide experimental validation of the scalability of our solution using an existing Linked Data privacy audit log model.