Decentralized bridge applications are important software that connects various blockchains and facilitates cross-chain asset transfer in the decentralized finance (DeFi) ecosystem which currently operates in a multi-chain environment. Cross-chain transaction association identifies and matches unique transactions executed by bridge DApps, which is important research to enhance the traceability of cross-chain bridge DApps. However, existing methods rely entirely on unobservable internal ledgers or APIs, violating the open and decentralized properties of blockchain. In this paper, we analyze the challenges of this issue and then present CONNECTOR, an automated cross-chain transaction association analysis method based on bridge smart contracts. Specifically, CONNECTOR first identifies deposit transactions by extracting distinctive and generic features from the transaction traces of bridge contracts. With the accurate deposit transactions, CONNECTOR mines the execution logs of bridge contracts to achieve withdrawal transaction matching. We conduct real-world experiments on different types of bridges to demonstrate the effectiveness of CONNECTOR. The experiment demonstrates that CONNECTOR successfully identifies 100% deposit transactions, associates 95.81% withdrawal transactions, and surpasses methods for CeFi bridges. Based on the association results, we obtain interesting findings about cross-chain transaction behaviors in DeFi bridges and analyze the tracing abilities of CONNECTOR to assist the DeFi bridge apps.