Waymo said it has been quietly conducting a small-scale trial over the past month in the Phoenix area.
The rebranded Google car division announced in a blog post late Monday it was taking applications to be part of its "early rider" program in Phoenix, the capital of the US state, and its suburbs.
"We'll be accepting hundreds of people with diverse backgrounds and transportation needs who want to ride in and give feedback about Waymo’s self-driving cars," said Waymo chief executive John Krafcik.
"The goal of this program is to give participants access to our fleet every day, at any time, to go anywhere within an area that's about twice the size of San Francisco."
Krafcik said as part of the trial Waymo was adding 500 hybrid minivans to its Arizona fleet -- which began with 100 vehicles -- as the group edges toward a ridesharing system similar to those offered by Uber, Lyft and others.
"We want as many people as possible to experience our technology, and we want to bring self-driving cars to more communities sooner," he said.
"Our early riders will play an important role in shaping the way we bring self-driving technology into the world -- through personal cars, public transportation, ride-hailing, logistics and more."
The tech giant has done extensive testing of the Google car, but in recent months has been working to adapt its software to operate on other vehicles -- using Chrysler Pacifica cars in Arizona.
Sergio Marchionne, CEO of Chrysler's parent company FCA, said the collaboration "has been advantageous for both companies as we continue to work together to fully understand the steps needed to bring self-driving vehicles to market."
Waymo said it has been quietly conducting a small-scale trial over the past month in the Phoenix area, taking participants to work, school, soccer practices and other activities.
Most major automakers and several other technology firms have been stepping up efforts on autonomous driving in recent years, contending these systems will eliminate the vast majority of road accidents. Apple is the latest to have obtain a testing permit in California.
German luxury carmaker Daimler and auto parts supplier Bosch announced plans this month to work together to create completely driverless cars in the next few years.
US-based Tesla is also stepping up efforts, as are several Chinese technology firms and the major US, Asian and European manufacturers.
The Google car already has undergone millions of miles of testing. But the latest drive appears to be part of an effort to challenge Uber head-on.
The two firms are in the middle of a heated legal battle, with Alphabet filing a lawsuit earlier this year accusing Uber of stealing its technology.
Waymo announced at the Detroit auto show this year that it would develop its self-driving technology with multiple partners, positioning itself as an automotive supplier.