The Aberdeenshire-based company said there had been an "unprecedented response" to its Equity for Punks USA crowdfunding initiative.
BrewDog hopes to raise up to $50m within six months to help fund expansion in North America.
Plans include a new 100,000 sq ft brewery in Columbus, Ohio.
It is scheduled to open later this year.
Shares in the funding round cost $47.50 each, with a minimum investment of $95. According to BrewDog, more than 1,200 people have already signed up to the scheme.
On its website, the company said: "This unprecedented response to our first crowdfunding round in the States shows the demand for our beer in America, and sets us up with a community of like-minded individuals ready and waiting to help us make our US business an explosive success."
Its Equity for Punks USA investment scheme is the fifth fundraising venture by the brewery, and its first in the US.
The Ellon-based company has raised more than £26m since launching its first Equity for Punks crowdfunding round in 2009.
Its last UK round raised £19m to fund growth plans, including expanding its brewery in Ellon and opening new bars. The round, which closed in April, fell short of its £25m target.
BrewDog's British business now employs more than 600 people globally and exports to 55 countries. It also operates more than 40 bars in the UK and overseas.

Veterans with amputation-related medical issues can now attend a clinic at the Surrey-based unit's Defence Medical Rehabilitation Centre (DMRC).
The first six such patients have already received treatment there.
Mr Fallon said the veterans who would be treated "have made enormous sacrifices to keep Britain safe".
He added: "This is about making sure they get the best possible treatment."
The six who have already received treatment were seen after referrals from their current NHS centre.
They had all experienced complex amputation-related complications.
While veterans' healthcare remains the responsibility of the NHS, they now have access to the DMRC at Headley Court near Epsom.
Staff there have acquired experience over the last decade in managing the rehabilitation of military casualties with complex trauma injuries.
The new set-up mirrors the tertiary referral system within the NHS, where one hospital can refer a patient to another hospital when needed.
The new programme will also develop existing collaboration with the NHS to ensure that knowledge and best practice are shared.

Staffordshire bull terrier Ziggy was found in remote woodland near Wansford in Peterborough on Wednesday morning.
X-rays showed the weapon had just missed his skull and vital organs.
RSPCA Insp Justin Stubbs helped a vet "slowly, slowly pull the bolt out" of the sedated dog. "It was a heart in the mouth moment but Ziggy is making a fantastic recovery," he said.
The two-year-old dog had been deliberately shot. It was "a very intentional shot at very close range", the RSPCA said.
It is thought Ziggy only survived by moving his head "at the right time".
An examination of his injuries showed Ziggy had been roaming the woods for a few days, "terrified and in complete agony", before being found by two walkers.
Despite having a 50cm (20ins) carbon fibre bolt embedded from one side of his head to the other, Ziggy was still wagging his tail and wanting people to make a fuss of him, Mr Stubbs said.
However, the vet was faced with the task of removing the weapon.
"It had missed Ziggy's brain, ears, eyes and skull bone by millimetres, but X-rays don't show up major blood vessels," Mr Stubbs said.
"It really was a heart in the mouth moment and hoping for the best, but we had everything in place in case anything happened."
When the bolt was slowly inched out, Mr Stubbs, the vet and a nurse realised it had not hit any blood vessels.
"I don't think anyone took a breath for about a minute. Then there was a collective sigh of relief," Mr Stubbs said.
"It had just gone through soft tissue and didn't even hit muscle."
Ziggy is now being looked after at nearby kennels where he is said to be making "a miraculous recovery".
"He is bounding around as if nothing happened," Mr Stubbs said.
"If ever a dog had a guardian angel, Ziggy had one that day."
The RSPCA is continuing to investigate and has appealed for information about the attack.
Craft brewer BrewDog has raised $1m (£770,000) from US investors within the first three days of a new funding round, according to the company.
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Veterans will now be treated at Headley Court military rehabilitation unit as well as serving personnel, Defence Secretary Michael Fallon says.
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The delicate operation to remove a crossbow bolt embedded in a dog's head took "just one minute", the RSPCA said.