Michael Bloomberg’s presidential campaign is hiring hundreds of workers in California to post regularly on their personal social-media accounts in support of the candidate and send text messages to their friends about him.

The effort, which could cost millions of dollars, is launching ahead of California’s March 3 primary and could later be deployed nationwide, according to people familiar with the matter and documents reviewed by The Wall Street Journal. It is among the most unorthodox moves yet by the heavy-spending billionaire...