Musk and Rogan had apparently been talking for more than two hours before Rogan offered Musk marijuana. He told Musk the rolled joint was marijuana wrapped in tobacco leaves.
Musk told Rogan he does not regularly smoke pot, saying he doesn't think it's very good for productivity. However, Musk took the joint from Rogan and smoked it.
During the interview, Musk said he was getting texts from friends asking what he was doing smoking.
Topics from their nearly four-hour conversation, which was uploaded to Rogan's YouTube channel, PowerfulJRE, ranged from artificial intelligence to space travel to the future of human civilization.
Meantime, Tesla's chief accounting officer, Dave Morton, is resigning after a month on the job because of the public attention and fast pace the post entails.
In a regulatory filing Friday, the electric vehicle maker reported that Morton has no disagreements with Tesla's leadership or its financial reporting.
RELATED: What exactly is a hyperloop?
Morton said in the filing he still believes in Tesla's mission and prospects.
The Palo Alto, California-based company said its chief financial officer and its corporate controller will oversee accounting functions.
For more stories, photos, and video on Tesla and Elon Musk, visit this page.
The Associated Press contributed to this report.