Anonymous cross-domain authentication schemes for Industrial Internet of Things (IIoT) have become a prominent research focus in recent years. However, existing schemes still face significant challenges, including the incompatibility of cross-domain authentication protocol and the unreliability of pseudonym management mechanism. To address these issues, this paper proposes TACA, a blockchain-based traceable and anonymous cross-domain authentication scheme. First, it introduces the InterPlanetary File System (IPFS) and blockchain to achieve a reliable pseudonym management mechanism, effectively avoiding deception during the tracing of malicious pseudonyms. Second, a compatible cross-domain authentication protocol is implemented based on Elliptic Curve Cryptography (ECC), which can be compatible with various intra-domain authentication mechanism without compromising the decentralization of each domain. Security analysis shows that the proposed scheme not only supports data confidentiality and unforgeability but also resists various attacks. Comparative results with multiple typical schemes in terms of security and performance indicate that the TACA scheme satisfies more security requirements while still maintaining lower computation and communication overheads.