Ride-hailing has become a vital component of urban transportation due to its flexibility and efficiency in meeting diverse passenger needs. Accurate demand estimation, particularly in identifying origin-destination (OD) pairs, is crucial for optimizing services for ride-hailing providers and drivers and ensuring efficient resource allocation. This study proposes an alternative approach to demand estimation using public transportation card data, addressing privacy concerns associated with directly collecting OD data from ride-hailing services. By analyzing hourly recorded departure and arrival data between administrative districts, the proposed statistical model estimates ride-hailing demand patterns, capturing both spatial and temporal dynamics across urban areas. Transportation data from selected urban districts in Seoul, Korea, was analyzed to validate this approach. Results demonstrate significant daily and hourly variations in demand, with distinct weekday commuting patterns and more balanced weekend flows, reflecting shifts between work-related and leisure activities. These findings highlight the model’s potential for accurately estimating demand without direct OD data, providing valuable insights for improving ride-hailing operations and supporting urban transportation planning. This approach can assist service providers in optimizing driver allocation and enhancing operational efficiency, contributing to the broader objectives of urban mobility management.