Other cryptocurrencies, including dogecoin – which has been promoted by high-profile Trump supporter Elon Musk – are also making gains.
In the run-up to the election Trump said he would create a strategic Bitcoin stockpile and appoint digital asset-friendly financial regulators.
Trump has said one of his first actions as president would be to sack the current chair of the Securities and Exchange Commission (SEC), Gary Gensler.
Mr Gensler, who was appointed Joe Biden in 2021, has led the SEC’s crackdown on the crypto industry.
Trump’s broader agenda, which includes cutting taxes and reducing regulations on businesses, has also driven a surge in other investments since he won the election.
Major stock indexes, the dollar and US bonds have all made gains in recent days.