The Florida governor and Mr. Musk set up an interview on Twitter Spaces, a live audio discussions platform.
But the discussion, scheduled for 6 o'clock Wednesday afternoon, was plagued by technical issues and the audio cut out before Mr. DeSantis could say a word.
Almost 20 minutes of glitches followed, before the exchange began.
Once the sound was stabilised, Mr. DeSantis declared that he is running for president of the United States.
By the time the talk had begun in earnest, hundreds of thousands of Twitter users had left the platform.
Since Mr. Musk took the reins at Twitter in October, he has laid off thousands of employees, including engineers responsible for the site's operations and technical troubleshooting.
Mr. DeSantis' team worked quickly to spin the technical stumbles, writing on Twitter that the announcement "broke the internet with so much excitement", and posting a link to the campaign website.
