Searching for available parking spaces is a major problem for drivers especially in big crowded cities, causing traffic congestion and air pollution, and wasting drivers' time. Smart parking systems are a novel solution to enable drivers to have real-time parking information for pre-booking. However, current smart parking requires drivers to disclose their private information, such as desired destinations. Moreover, the existing schemes are centralized and vulnerable to the bottleneck of the single point of failure and data breaches. In this paper, we propose a distributed privacy-preserving smart parking system using blockchain. A consortium blockchain created by different parking lot owners to ensure security, transparency, and availability is proposed to store their parking offers on the blockchain. To preserve drivers' location privacy, we adopt a private information retrieval (PIR) technique to enable drivers to retrieve parking offers from blockchain nodes privately, without revealing which parking offers are retrieved. Furthermore, a short randomizable signature is used to enable drivers to reserve available parking slots in an anonymous manner. Besides, we introduce an anonymous payment system that cannot link drivers' to specific parking locations. Finally, our performance evaluations demonstrate that the proposed scheme can preserve drivers' privacy with low communication and computation overhead.