Musk has fully owned Twitter since October 27 and has repeatedly courted controversy as CEO, sacking half of its staff, readmitting far-right figures to the platform, suspending journalists and trying to charge for previously free services.
"I will resign as CEO as soon as I find someone foolish enough to take the job!" Musk tweeted, saying he will then only run software and server teams at Twitter.
In the poll results which were posted on Monday, 57 percent of voters, or 10 million votes, favored Musk stepping down just weeks after he took ownership of the company for $44 billion.
Musk has used the Twitter polls to take other decisions on the platform, including the reinstatement of the account of former U.S. president Donald Trump and other suspended users.
Earlier this week he used a laughing emoji to ridicule a report he was in search of someone to take over as boss of Twitter, and tweeted that "no one wants the job who can actually keep Twitter alive."
Analysts have pointed out that the stock price of his electric car company Tesla has slumped by one-third since Musk's Twitter takeover, and some suggest Tesla's board was putting pressure on him to quit his Twitter role.
"Finally a good step in the right direction to end this painful nightmare situation for Tesla investors," said Wedbush analyst Dan Ives on Tuesday.
In discussions with users after posting his latest poll, Musk had renewed his warnings that the platform could be heading for bankruptcy.
Policy by poll?
The unpredictable entrepreneur posted his poll on his resignation shortly after trying to extricate himself from yet another controversy.
On Sunday, Twitter users were told they would no longer be able to promote content from other social media sites.
But Musk seemed to reverse course a few hours later, writing that the policy would be limited to suspending accounts only when that account's "primary purpose is promotion of competitors."
The attempted ban prompted howls of disapproval and even bemused Twitter cofounder Jack Dorsey, who had backed Musk's takeover.
Analyst Ives noted that "advertisers have run for the hills and left Twitter squarely in the red ink potentially on track to lose roughly $4 billion per year."
Shortly after taking over the platform, Musk announced it would charge $8 per month to verify account holders' identities, but he had to suspend the "Twitter Blue" plan after an embarrassing rash of fake accounts. It has since been relaunched.
On November 4, with Musk saying the company was losing $4 million a day, Twitter laid off half of its 7,500-strong staff.
Musk also reinstated Trump's account -- though the former US president indicated he had no interest in the platform -- and said Twitter would no longer work to combat Covid-19 disinformation.
In recent days, he suspended the accounts of several journalists after complaining some had published details about the movements of his private jet, which he claimed could endanger his family.
Some of the suspended accounts have since been reactivated.
On Monday, the head of the European Parliament, speaker Roberta Metsola, sent a letter to Musk inviting him to testify before the legislature, her spokesman said.
The parliament has no power to compel Musk to turn up, and his response was not immediately known.