With the popularity of cloud storage, integrity verification for outsourced data has attracted more and more attention. The majority of existing research works rely on a unique third-party auditor (TPA) or fixed TPAs to audit the integrity of outsourced data, and thus they are vulnerable to DoS and collusion attacks as the TPA is not completely trusted. To conquer this problem, a blockchain-based random auditor committee is proposed to replace the fixed TPAs for the integrity verification (call scheme for short). The proposed blockchain consensus algorithm utilizes a verifiable random function (VRF) to select the third-party auditor committee (TPAC) which performs contract verification. The leader of TPAs (LTPA) packs the verification proof into a blockchain called verification chain. The main idea is employing the output of a VRF for leader election to make it probabilistic, such that specific nodes cannot be targeted in advance and a certain fraction of the nodes being malicious can be tolerated. We present rigorous security analysis to demonstrate the security of the proposed scheme. Meanwhile, the comprehensive performance evaluation shows that the proposed scheme improves the performance of data integrity verification effectively.