TOKYO—Nissan Motor Co. plans to start testing robo-taxis on Japanese streets in March with the aim of launching a self-driving taxi service, as Japan’s top car makers struggle to keep pace with Detroit and Silicon Valley.

Nissan said at the start of the year that it was teaming up with Tokyo software company DeNA Co. to build a fleet of self-driving Leaf electric cars that could be summoned using a smartphone application. With Tuesday’s announcement, the auto maker has laid out its first concrete plan to get those vehicles...