By Brendan O'Brien

MILWAUKEE (Reuters) - A Wisconsin appeals court on Thursday ruled the state's controversial voter ID law is constitutional, a victory for supporters who say the measure limits fraud at the ballot box.

The Fourth District Court of Appeals overturned a March 2012 decision by Dane County judge Richard Niess, who ruled in favor of the League of Women Voters of Wisconsin, which claimed that the law is too burdensome, denying potential voters the right to vote.

The organization "makes no effective argument that, on its face, the requirement makes voting so difficult and inconvenient as to amount to a denial of the right to vote," the appeals court wrote in its decision.

The Wisconsin measure, passed in 2011 by a Republican-controlled legislature, requires voters to present photo identification such as a driver's license at polling places for federal, state and local elections.

The law, which still faces legal challenges, would put Wisconsin among nearly three dozen U.S. states with voter ID measures, according to the National Conference of State Legislatures. A hot-button political issue, Republicans say voter ID laws prevent election fraud while Democrats say they hinder low-income and minority voters.

The League of Women Voters of Wisconsin is considering its options with regard to further legal review, Andrea Kaminski, the organization's executive director, said in a statement.

"We're going to take some time and review the substance of the decision and decide whether or not to petition the Wisconsin Supreme Court," said Lester Pines, the attorney for the League of Women Voters of Wisconsin.

The law is currently not in effect as another state appeals court has yet to decide on different challenge. Two federal lawsuits also are pending on the state's voter ID law.

"While today's decision is an important step toward full vindication of the law, we recognize that other challenges are still pending that address different issues," said Wisconsin Attorney General J.B. Van Hollen, a Republican, in a statement.

Voters were required to show ID during a February primary before the court injunctions went into effect. The law was not enforced when Republican Governor Scott Walker survived a recall election last June and during the general election in November.

In April, Republican lawmakers in Arkansas voted to override a veto by the state's Democratic governor and approve a similar bill that requires voters to show photo identification at the polls.

(Reporting by Brendan O'Brien; Editing by Paul Thomasch and Richard Chang)