The increasing amount of personal data is raising serious issues in the context of privacy, security, and data ownership. Entities whose data are being collected can benefit from mechanisms to manage the parties that can access their data and to audit who has accessed their data. Consent management systems address these issues. We present Consentio, a scalable consent management system based on the Hyperledger Fabric permissioned blockchain. The data management challenge we address is to ensure high throughput and low latency of endorsing data access requests and granting or revoking consent. Experimental results show that our system can handle as many as 6,000 access requests per second, allowing it to scale to very large deployments.