SAN FRANCISCO—Uber Technologies Inc. is testing a new feature that allows some drivers in California to set their fares, the latest in a series of moves to give them more autonomy in response to the state’s new gig-economy law.

Starting Tuesday morning, drivers who ferry passengers from airports in Santa Barbara, Palm Springs and Sacramento can charge up to five times the fare Uber sets on a ride, according to a person involved in developing the feature. Uber confirmed in an emailed statement that it is doing an “initial test”...