It is hoping to raise funds towards their conservation and a major project to digitalise the ancient texts.
The Dead Sea Scrolls were discovered in a cave in Qumran on the West Bank in 1947 and include the oldest known surviving biblical texts in the world.
There are more than 15,000 Dead Sea Scrolls, written on parchment in Hebrew, Aramaic and Greek, and dating from between 150BC to 70AD.
According to the Daily Mail, people will be able to adopt a page for £1,200 and have a dedication plaque with their name on it displayed when the text is exhibited.
Jacob Fisch, of the Friends of Israel Antiquities Authority in New York, said the scheme would raise money for conservation, cleaning and high-resolution photography of the scrolls.
"We want to conserve all the scrolls and eventually put them online, and digitisation is part of a multi-stage project. Most people who sign up want a medium fragment," he said.
"It's like people adopting animals from a zoo- they are more likely to want a lion than an ant.
"We will work with people's budgets to find them something – there are 15,000 fragments to pick from.
"People love the idea of adopting a chapter from Leviticus or Deuteronomy."