For the first time, an accident involving one of Cruise’s self-driving cars in San Francisco injured a motorist, according to a report the company filed with state regulators.

The injury, to a motorcyclist who was lane-splitting and trying to pass the Cruise car, was minor, according to the report. Cruise also cites a San Francisco Police Department collision report that found the motorcyclist to be at fault.

Cruise has steadily expanded the testing of its autonomous vehicles since General Motors acquired the San Francisco startup last year. The cars — specially made electric Chevy Bolts — have become a frequent sight around San Francisco, whose crowded and hilly streets Cruise considers an ideal testing ground.

As the number of test miles driven has increased, Cruise has filed a number of collision reports with the California Department of Motor Vehicles. All of the others have described minor fender-benders.

The latest report details an accident that occurred on Dec. 7.

A Cruise car operating in autonomous mode was heading east on Oak Street just past the intersection with Fillmore Street, traveling in the middle of three lanes. The car sensed an opening in the left lane, between a minivan in front and a sedan behind, and started to merge into the left lane. The minivan, however, slowed down and narrowed the opening, so the Cruise car shifted back to the center lane.

As it did so, a motorcyclist who had been lane-splitting between the center and right lanes moved to the center, “glanced the side of the Cruise AV, wobbled, and fell over,” according to the report. The car had been traveling at 12 mph at the time of the accident, while the motorcyclist was estimated to be traveling at 17 mph.

The motorcyclist stood up and walked his cycle to the side of the street. He and the Cruise employees exchanged information, while 911 was called. The motorcyclist complained of shoulder pain and was taken to receive medical treatment. The collision left a long scuff on the side of the car.

“At Cruise, we test our self-driving cars in challenging and unpredictable environments precisely because by doing so we will get better, safer AV technology on the roads sooner,” said GM spokeswoman Stephanie Rice, commenting on the report. “In this case the motorcyclist merged into our lane before it was safe to do so.”

David R. Baker is a San Francisco Chronicle staff writer. Email: dbaker@sfchronicle.com Twitter: @DavidBakerSF