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.
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.