The retired neurosurgeon, who grew up in a poor family before winning a scholarship to Yale University, has fanned controversy in the United States for anti-Muslim and anti-refugee remarks.
"Dr Carson and a small group are in Jordan," a campaign official told AFP on condition of anonymity.
"He is there fact finding, listening, learning and meeting. No public or press events planned."
Carson is to visit a UN-run Syrian refugee camp northeast of the Jordan capital early on Saturday, a Jordanian security source told AFP on condition of anonymity.
More than four million Syrians have fled the civil war, with more than 600,000 of them in Jordan, the United Nations refugee agency estimates. America has so far accepted just 2,283.
Yet the plight of Syrian refugees has become a political hot potato in America with half the nation's governors declaring Syrian refugees persona non grata after the Paris attacks.
Signup to our newsletter and follow us on Facebook and Twitter!
Carson told The New York Times, which first reported the visit, that he wanted to get a better understanding of the refugee issue and burnish his foreign policy credentials.
"I find when you have firsthand knowledge of things as opposed to secondhand, it makes a much stronger impression," he was quoted as telling the paper before his departure late Thursday.
Last week, he compared refugees fleeing the nearly five-year war in Syria to rabid dogs.
"We must balance safety against being a humanitarian," Carson said during a campaign stop in the southern US state of Alabama.
"If there's a rabid dog running around your neighborhood, you're probably not going to assume something good about that dog. And you are probably going to get your children out of the way."
He also followed the lead of rival candidate Donald Trump in saying that he too saw a video of Arab Americans cheering as New York's World Trade Center collapsed on September 11, 2001.
Elected officials, police and fact-checkers have debunked the rumors, which come as community activists complain of an "unprecedented" anti-Muslim backlash in America following the Paris attacks.