PHOENIX — Americans upset about illegal immigration have a new outlet for their rage: a fund set up by the State of Arizona that will use private donations to build a border wall.

Critics call the state’s effort to build its own border barriers a foolhardy, feel-good campaign that will have little practical effect on illegal border crossings. But organizers in the State Legislature, which created the fund, say it will allow everyday people fed up with the inability of Congress to address the problem of illegal immigration to contribute personally to a solution.

Beginning during the second Bush administration and continuing in President Obama’s tenure, the federal government has built more than 600 miles of barriers, some designed to keep out cars and others to block individuals from crossing. The congressionally approved construction effort is winding up, but about 82 miles of Arizona’s 388 miles of border remain without a barrier, federal officials say.

The construction has been expensive. The Government Accountability Office said in a 2009 report that the federal government spent $1 million to $3 million for every mile of border fencing. Arizona, though, intends to use low-cost inmate labor to reduce those costs.