A small autonomous-cars company owned by General Motors Co. is getting into the high-definition mapping business, a move that could help the Detroit auto giant compete with Google and others in the race to develop self-driving vehicles.

Cruise Automation, the San Francisco startup GM bought last year, is recruiting a leader for a fledgling mapping unit, according to the company’s website. The role involves overseeing a fleet of mapping vehicles, collection of data needed to lower dependence on human drivers and the creation...