State Sen. Steve Smith, a Republican who sponsored the legislation, said he hopes to raise more than $50 million from donors across the United States, The (Phoenix) Arizona Republic reported.
"Donate to the country's security," Smith said. "This is an American problem, not an Arizona problem."
Arizona is the first state to try such a security tactic, officials said.
State lawmakers who back the measure have said they want a solid, multilayer fence high enough to keep out pedestrians along the state's approximately 370-mile border with Mexico. Smith said the effort also could incorporate more high-tech security efforts.
Fencing between Yuma and Nogales in western Arizona is the type of barrier lawmakers want, the Republic said. The rest of the border has either no fencing or has fencing designed to bar vehicles. Smith said most illegal immigrants cross in eastern parts of Arizona that have a less secure border.
Smith said Arizona's final cost would depend on the type of fence constructed and whether the state can get private companies to donate some of the supplies.
Securing landowner permission will determine where the fence can be built, the Republic said. Much of the Arizona border is on federal land or Indian reservations, with small portions privately owned. The federal government allowing the fence to be built within a 60-foot easement along the border would be the easiest solution for getting the land, Smith said.
The Sierra Club opposes the law, saying Arizona already has more border walls than any other state and the walls have caused flooding in some areas and have blocked wildlife elsewhere.