During the course of a wide-ranging chat with Rogan, Musk drank whiskey and tried a marijuana-and-tobacco cigarette proffered by the comedian.
He told Rogan he thinks that merging humans with computers is the approach that "seems probably the best for us: if you can't beat it, join it". Rogan then said "it's totally legal", and Musk said "OK" and took a drag.
Marijuana is legal for medical and recreational use in California, where the interview took place.
Tesla's accounting will be overseen by its chief financial officer and its corporate controller, the company said.
Elon Musk has added another bit of freakish behaviour to the list by smoking a joint during a live interview. "It just wasn't the way I operate", he said.
Musk said he is less anxious about AI than he had been, mostly due to "taking a more fatalistic attitude".
During the interview, the pair discussed Musk's ability to dream up ideas and inventions, with the billionaire comparing the way his brain works to a "mutation", saying when he was a child he thought he was "insane".
After the podcast aired Tesla shares dropped 9 per cent, wiping $3.1 billion off the company's value (at the time of writing.) Although, that may have more to do with Musk's robotic behaviour than smoking weed.
In July he shocked investors by announcing on Twitter that he had funding secured to take his vehicle firm Tesla private. His first day, August 6, was two days before CEO Elon Musk's now-infamous tweet about taking Tesla private that has ended in lawsuits and investigations by federal regulators.
During the podcast interview, Musk, who is also the founder of the startup Boring Co., as well as Neuralink, said that running Tesla has been the hardest of his current projects. This story was made possible by generous people like you.
Tesla's chief accounting officer, Dave Morton, said he was leaving the company after considering the level of attention Tesla has received and the "pace within the company".
"I think people should be nicer to each other", he said. "As a result, this caused me to reconsider my future".