Alphabet Inc.’s Google has quietly opened its Waze ride-sharing service to San Francisco-area users, expanding a pilot program and confirming the company’s interest in the lucrative ride-hailing industry.

Smartphone users in the San Francisco area now can download a mobile app called Waze Rider to request rides to and from work from drivers using Google’s popular Waze navigation app. Google in May launched a test of the carpool service for workers at several area employers, but the service has been gradually rolling out to...