The valuation caps a strong month for the virtual currency, with its value growing by more than 65% in a month.
The steady rise in value is believed to be linked to policy changes in Japan and China that have made it easier for speculators to trade in bitcoins.
Many other virtual currencies have also enjoyed a sustained rise in value over the last few weeks.
Bitcoin first broke the $1,000 (£768) barrier in November 2013 but its value has fluctuated wildly since then. For instance, in early 2014 one bitcoin was worth only $280 (£215).
And at the end of 2016, each one was changing hands for about $900 (£690).
Bitcoin emerged in 2008 and is a digital currency based around cryptography. Individual coins can be split into smaller denominations and many people involved with the currency use computers to verify the globally-held log, known as the blockchain, of who spent what where.
Verifying transactions involves solving a complicated mathematical problem and the first person to do so gets rewarded with bitcoins.
Rising interest in bitcoin has sparked the creation of many other crypto-currencies. These have proved popular as the technology underlying bitcoin has struggled to cope with its popularity and growth. One estimate suggests bitcoins now make up only 47% of all traded crypto-currencies.
Rivals such as Ethereum and Ripple have been gaining value far faster than bitcoin over the last few months.
The surging valuations has led some commentators to suggest that an unsustainable crypto-currency bubble is developing.
"The question is not if but when the market will turn," said an editorial in The Economist.

South Yorkshire MP Angela Smith said Barnsley businessman Tony Hickton's idea to improve transport links would need to provide value for money.
Mr Hickton said current routes between the two cities were not good enough.
He said a road and rail tunnel from around junction 36 of the M1 to the M67 would boost the economy.
The Penistone and Stocksbridge Labour MP said: "The economic impact of improving the link between Sheffield and Manchester shouldn't be underestimated.
"You can't put motorways through national parks, we've got to protect those very precious landscapes.
"If you stand above the Woodhead Pass and look down on it and see all those HGVs, it's a real blight on that beautiful landscape, and anyone who uses the road knows how difficult it is to use.
"So clearly there has to be a solution somewhere along the line to this problem."
Mr Hickton, from construction inspection company Hickton, said it could be built using a mixture of private and state funding.
He added: "These tunnels won't be built tomorrow, but if we don't press the button now, we'll never be ready, so why not now?"

The Ramsdens Discount Department Store on Cleethorpe Road was opened in 1946.
The company said there would be some redundancies, but added it hoped "to be able to offer alternative employment to some employees".
Last year planning permission was granted by North East Lincolnshire Council to redevelop the site into a new retail park.
The store is expected to close over the summer.
In a statement, the firm's directors said the store had "continued to decline in what has become a very tough and competitive local market".
It added its nearby Home Interiors store would continue to trade.
The value of Bitcoin has hit a new high with each individual coin now worth more than $2,100 (£1,615).
[NEXT_CONCEPT]
A proposal to build a tunnel through the Peak District, linking Sheffield and Manchester, should be looked at according to the area's MP.
[NEXT_CONCEPT]
Up to 47 jobs are at risk after a Grimsby shop confirmed it is to close after nearly 70 years of trading.