A federal judge on Friday gave the go-ahead to a lawsuit against the social media company X, formerly known as Twitter, in which workers claim that the company promised but never paid millions of dollars in bonuses.

In June, Mark Schobinger, a former senior director of compensation for Twitter who lives in Texas, sued the company, claiming breach of contract under California law. The company has its headquarters in San Francisco.

Mr. Schobinger said that both before and after the billionaire Elon Musk bought Twitter last year, the company had orally promised employees 50 percent of their 2022 targeted bonuses if they stayed with the company in the first quarter of 2023. However, the bonuses were never paid, according to the suit.

Mr. Schobinger filed the suit on his own behalf and on behalf of nearly 2,000 other current and former workers. The amount in dispute is greater than $5 million, according to court records.