But experts say it is accepted science that they were tombs for pharaohs.
Mr Carson is a retired surgeon who has unexpectedly risen to the top of the Republican primary race in some polls.
Video posted online on Wednesday by Buzzfeed News shows Mr Carson explaining his theory 17 years ago at a Michigan college affiliated with his Seventh-day Adventist Church.
In the video, Mr Carson says: "My own personal theory is that Joseph built the pyramids in order to store grain."
He was referring to the Old Testament story of Joseph predicting famine and advising the pharaoh to store surplus food.
Mr Carson said that is more likely than the accepted archaeological conclusion that the massive structures were built as tombs for pharaohs.
At a book signing on Thursday in Florida, Mr Carson stood by his statement.
"Some people believe in the Bible like I do and don't find that to be silly at all, and believe that God created the Earth and don't find that to be silly at all," Mr Carson said.
"The secular progressives try to ridicule it every time it comes up and they're welcome to do that."
Calling the grain theory his "personal belief", Mr Carson said, "I happen to believe a lot of things that you might not believe because I believe in the Bible."
Neither Mr Carson's church nor any other major Jewish or Christian sect shares his belief about the pyramids' origins.
Jodi Magness, a specialist in biblical archaeology at the University of North Carolina-Chapel Hill, said she knows of no scholar or archaeologist who questions that the pyramids were used as royal tombs.
"This is not an academic topic of debate," Ms Magness said. "The use of the pyramids as tombs is verified by both written (literary) sources and archaeological evidence."
The pyramids were built with narrow, secret passages intended to foil grave-robbers, making the structures unsuitable for grain storage, Ms Magness added.
And the design of the pyramids, with associated temples, "reflects the ancient Egyptian concept of the cosmos, according to which the king or pharaoh was at the centre of a unified kingdom, serving as a god, a political ruler and a divine mediator."
Daniel Weber, a spokesman for the Seventh-day Adventist Church, said Mr Carson's belief about the pyramids are "his own interpretation".
"Of course, we believe in the biblical account of Joseph and the famine," Mr Weber said. "But I've never heard the idea that pyramids were storehouses of grain."
Mr Carson acknowledged in his 1998 speech that "all the archaeologists" say the structures were built as tombs, but he argued that the "hermetically sealed" chambers found in the pyramids "would have to be that way" to store grain.
Mr Carson speaks often about his faith and has written extensively about his beliefs in his books. His popularity among evangelical Christian voters has helped fuel his rise in the Republican primary.
He has garnered attention previously for stating that, despite his scientific training as a neurosurgeon, he rejects evolutionary biology.
Another top contender for the Republican nomination, businessman Donald Trump, has suggested that Mr Carson's religious beliefs put him outside mainstream American Christianity.
At a rally in Florida last month, Mr Trump called his own Presbyterian church "middle of the road" before adding, "I mean, Seventh-day Adventist, I don't know about."
In an interview conducted after Mr Trump's remarks, Mr Carson said he expects in politics to have his religious affiliation questioned, but he defended his faith and his church.
"There are a lot of people who have a close relationship with God, and you can generally tell who they are by the way they act, the way they treat other people," he said.
"The reason that there are like 4,000 denominations is that people have looked at this and said, 'Let's interpret it this way. Let's interpret it this way.'
"Sometimes they get caught up in that and forget about the real purpose of Christian faith," he concluded.
A first-time political candidate, Mr Carson has a penchant for headline-grabbing statements beyond matters of faith.
He has equated abortion and the Affordable Care Act to slavery, compared the zeal of Islamic State militants to that of American Revolution patriots and suggested that the Holocaust may not have occurred had European Jews been better armed against the Nazis.