THE United Nations is marching into uncharted territory with its commitment to carry out the Cambodian peace agreement signed last week in Paris. The UN not only must supervise a cease-fire, disarm the warring sides, and oversee free elections, it must also help administer the country in the period before elections, scheduled for early 1993.As many as 20,000 UN peacekeeping troops and civilian administrators could be heading toward Cambodia. Their work will not be easy, and they may have to use their guns in the months ahead. Artillery battles between government forces and one of the opposition factions flared the day after the Paris signing. For now, however, the roar of howitzers is muffled. After more than a decade of constant war, the combatants in Cambodia have agreed on a treaty. The cold war's end and a lessening of friction between China and Vietnam helped open the way toward peace. Outside powers whose rivalries fueled the war decided to nudge their Cambodian clients toward accommodation. But will China continue to press the Khmer Rouge toward peaceful power-sharing and away from schemes to seize absolute control in Phnom Penh? Beijing has no interest in seeing genuine democracy evolve in Cambodia, but it has a definite interest in being perceived as a constructive member of the world community. The Khmer Rouge is ever the wild card in Cambodia. Recent moves to force refugees back into parts of Cambodia it controls reveal a continuing penchant for cruelty. Yet the Khmer Rouge's military strength dictates its inclusion in the peacemaking process. The Khmer Rouge will be represented on the Supreme National Council that will govern jointly with the UN. That role, however, can't obscure the Khmer Rouge's horrific past. US Secretary of State James Baker, addressing the Paris conference, tried to rule out any return to power by Pol Pot or other Khmer Rouge figures who orchestrated the slaughter of more than 1 million Cambodians in the late '70s. The American record with regard to the Khmer Rouge is tarnished; many believe that US aid to the rebels fighting the Vietnam-backed regime in Phnom Penh often fell into Khmer Rouge hands. Forceful US support for the UN mission to bring peace to Cambodia could help correct that re cord. Recent UN triumphs, such as the launching of an independent Namibia, brought recognition of the international body's value in a world freed from superpower tensions but assailed by regional conflict. Success in Cambodia would establish that value beyond any doubt.