Even if the referendum passed, the application for membership would still need General Assembly approval and the Security Council's recommendation, which is unlikely given China's seat on the council.
Taiwan was expelled from the UN in 1971 when its seat was transferred to the Beijing-based Chinese government.
David Lee, a spokesman for Taiwan's president, said on Wednesday that the first stage had started and "we have already begun collecting the signatures".
One million signatures are needed to get the issue on the ballot in one of the island's two forthcoming elections.
Taiwan split from mainland China at the end of the Chinese civil war in 1949
Beijing regards Taiwan as part of its territory, and says it will use force if it ever declares independence
Beijing and Taipei both say they are the legitimate government of all China
Taiwan has been a multi-party democracy since 1996
Taiwan's defence ministry says China now has nearly 1,000 missiles aimed at the island
The US is the major arms supplier to Taiwan and has warned China that any attack on the island would be viewed with "grave concern"
On Monday Chen Shui-bian, the president, said he "hoped" to run the referendum alongside either the parliamentary polls in January or the presidential vote in March.
Reacting to Chen's comments, Sean McCormack, the US state department spokesman, said the US objected to "any initiative that appears designed to change Taiwan's status unilaterally".
He said the referendum would not change Taiwan's UN status but "would increase tensions in the Taiwan Strait".
"Maintenance of peace and stability across the Taiwan Strait is of vital interest to the people of Taiwan and serves US security interests as well," he said.
McCormack said such a vote "would appear to run counter" to Taiwan's repeated pledges to the US and the international community that it would not change the status quo with China.
"Consistent with our one-China policy, we do not support Taiwan's membership in international organisations that require statehood, including the United Nations," he added.
Washington, by law, has to help defend Taiwan if it is attacked by China.
In May, the World Health Organisation rejected a fresh bid by Taipei to apply for membership under the name "Taiwan".
China's UN allies far outnumber those of Taiwan, which is now recognised by just 24 countries around the world.
On Wednesday, Chen welcomed his Guatemalan counterpart, Oscar Berger, at an elaborate ceremony, extolling the close relations between the two countries.
The visit comes as Taiwan struggles to maintain its shaky diplomatic position, which received a heavy blow this month when longtime Latin American ally Costa Rica announced that it was changing its recognition to rival China, prompting fears of a collapse in its regional diplomatic standing.