Recent advancements in vehicular traffic sensing have significantly enhanced traffic information collection for the platform. However, this approach encounters two primary challenges: balancing the freshness of traffic information in the long term with the costs of vehicle recruitment and ensuring the privacy of participating vehicles. To address these challenges, we introduce a smart-contract-based incentive mechanism that recruits vehicles for traffic sensing. Our approach is structured as a two-stage game. In Stage I, the platform designs the incentive mechanism. In Stage II, vehicles independently decide their participation in the sensing process. Despite the inherent challenges of dealing with different time scales and the lack of future information, our framework effectively transforms the long-term problem into a solvable short-term one with a closed-form solution. Additionally, our implementation of the incentive mechanism through a blockchain-based smart contract offers a unique advantage: it enables vehicles to anonymously upload sensing data and receive payments, thereby safeguarding their privacy. Numerical analysis demonstrates the efficacy of the proposed method in fulfilling long-term information freshness requirements. Furthermore, the proposed method reduces the platform's time-average cost by 59.6%, 24.6%, 28.5%, and 25.8%, compared with other benchmarks.