Mr Musk's poll received more than two million responses in five hours since he posted it. It comes just days after the billionaire said that SpaceX would accept dogecoin as payment to launch a lunar mission next year.
Based on current prices, nearly 80,000 dogecoins - or 0.7 bitcoin - would be needed to buy the cheapest Tesla Model 3 car.
Dogecoin jumped more than 700 percent over the last month and is now the fourth-largest cryptocurrency.
Last Thursday, the cryptocurrency hit a record high of above $0.73.
Shares of Tesla were down by four percent in early trading after the company halted plans to buy land to expand its Shanghai plant.
Over recent months, Mr Musk’s social media influence has helped to move financial markets.
Earlier this year, Tesla converted $1.5billion to Bitcoin and the company announced they were offering it as a payment method across the US.
The Tesla boss confirmed the news on Twitter and said payments to Tesla will "be retained as Bitcoin".
Mr Musk tweeted: "You can now buy a Tesla with Bitcoin.
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Mr Musk said on Clubhouse: “I am late to the party but a supporter.
“I think Bitcoin is on the verge of getting broad acceptance by conventional finance people.”
He added: “Many friends of mine have tried to convince me to get involved in Bitcoin for a long time."
He then posted: "In retrospect, it was inevitable."
The price of dogecoin rose by 50 percent minutes after the Tesla chief executive tweeted: “Dogecoin is the people’s crypto”.
He then added: “No highs, no lows, only Doge”.
Mr Musk also tweeted a member of himself and dogecoin in Disney’s Lion King.
He also said previous comments about dogecoin were “really just meant to be jokes”.
Bitcoin’s price rose above $38,000 after the Tesla boss changed his Twitter biography to “#bitcoin” earlier this year.
In February, the electronic car company announced it had bought $1.5billion (£1.1billion) in the cryptocurrency.
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