THE CONTRA AID votes today and tomorrow in Congress can help advance Nicaragua toward peace and democracy. The Sandinistas, their economy devastated and their people divided, have already offered to let the resistance stay constituted and armed in a cease-fire and to continue (direct) cease-fire talks even if aid is approved. The contras have stopped demanding that the Sandinistas pay in heavy political concessions just for a cease-fire. President Reagan has reduced his aid request to dimensions that make conservatives fear he is undercutting the great strategic stakes he insists are in the balance.

Sen. Chris Dodd makes the case against aid on the opposite page today. He does not make the claim some others do that the contras are CIA stooges, mercenaries, terrorists and Somocistas -- labels that have become increasingly inapplicable as the contras have sought to clean up their act and earn support in the countryside. His main argument is the widely heard plea to ''give peace a chance.''

Some part of this plea arises from a legitimate concern that contra aid and the impetus it gives to continued battle could sink Central America's plan for peace and democracy. Another part appears to arise out of the current, furious debate over whether the Sandinistas' partial steps toward a political opening result exclusively from Central American diplomacy or from the peace plan and contra pressure. Mr. Dodd and like-minded Democrats say contra aid has not helped, it's hurt, and it will keep hurting. This is an arguable claim, but we think the evidence finally goes the other way. Much has changed since Central American diplomacy became a factor last summer. The record of the last six months demonstrates, we believe, that a carrot-and-stick combination has moved the Sandinistas. With cease-fire talks scheduled to resume next week, this is no time to demobilize the forces of one side alone. We think the same combination can move the Sandinistas further, without capsizing the peace plan, and on that basis we support the president's request.

It remains a gamble whether a Marxist party can move back toward democracy -- in a country and region with pitifully little democratic experience. But it is a gamble worth taking: the Sandinistas have yet to consolidate their power, and their neighbors have a paramount interest in urging democracy upon them.

The Arias plan has two inseparable and equally vital parts: democratization and the establishment of peace. In tandem with Nicaragua, but not on its own, this country should be moving to fulfill its part of the obligation.