Uber Technologies Inc. is moving a test of its self-driving cars to the friendlier environs of Arizona after suffering a regulatory defeat in California over its use of the vehicles in San Francisco.

The startup on Thursday said it would begin a test of the self-driving vehicles early next year in Phoenix, and it sent journalists photos of the vehicles leaving a warehouse hauled by a big rig. Uber touted the support for its experiment of Arizona Gov. Doug Ducey, a Republican, who had issued a statement telling Uber “California...