The New Jersey legislature acted swiftly and overwhelmingly yesterday to make the state the first to ratify the proposed constitutional amendment that would give the District of Columbia full voting representation in Congress.

"We are off and running," D.C. Del. Walter Fauntroy said jubilantly after the ratification was approved by votes of 59-to-12 in the Assembly and 27-to-5 in the Senate.

Fauntroy, who led a delegation of District supporters to the state house, recalled that "a journey of 1,000 miles begins with one step and we took that one step here today."

A total of 38 states must ratify the proposal within seven years before it can become an amendment, probably the 27th to the U.S. constitution.

The Pennsylvania legislature is scheduled to initiate the ratification procedure in Harrisburg today, but a vote there is not expected until the resolution has cleared a committee process that could take a week or more.

New Jersey legislators reacted to appeals froms tate and District officials that the state be the first to ratify, following the refusal of California and Delaware to be first to affirm last month. Gov. Brendan T. Byrne and other state political leaders lobbied intensively on the amendment's behalf.

In a ceremony in his office following the vote, Byrne, who had no official role in the ratification process, signed a letter to President Carter informing him of the action and expressing hope that it "will be followed by similar action around the nation so that an old inequity is righted and the 700,000 residents of the District will receive full voting rights."

Rep. Peter W. Rodino (D-N.J.), whose House Judiciary Committee conducted hearings on the issue and then sent it to the floor for a vote last spring, called yesterday's vote "a proud moment in the history of our state."

"The beauty of our constitutional system is its ability to respond to the changes of history," Rodino said. "This is an idea whose time has come. The Congress initiated this process of change and New Jersey has responded to the call. It has acted wisely, courageously and in the best interest of American democracy."

Opposition to ratification in the New Jersey legislature was similar to that voiced by some members of the California and Delaware legislatures late last month: there was no justification for a speedy vote just so their respective states could be first. Republican opponents in both houses here attempted to delay action by referring the resolution to committees, but both attempts were roundly rejected.

Assemblyman William F. Dowd's (R-Allenhurst) attempt yesterday to send the proposal to the Judiciary Committee met decisive opposition from Speaker Christopher Jackman and was defeated by a vote 21-46.

When the Assembly voted for ratification a moment later, Jackman called Fauntroy and Rodino to the podium and shook their hands. Among those applauding in the gallery were John W. Hechinger, the Democratic national committeeman from the District, and Robert Linowes, president of the Metropolitan Washington Board of Trade.

Senate President Joseph P. Merlino then came to the podium and personally carried the resolution down the hall to his chamber, where ratification was completed 45 minutes later.

The whole procedure took only 99 minutes, from introduction of the resolution by Assemblyman Peter Shapiro (D-Irvington) until the Senate vote at 4:13 p.m.

Despite some Republican opposition, the resolution received bipartisan support. All but one Democrat and about half the Republicans in both supported it.

Fauntroy thanked Byrne, whose top aides lobbied both houses for approval and Republican and Democratic legislative leaders "on behalf of three-quarters of a million people who, after 200 years, still endure the tyranny of taxation without representation. You are the first to correct this historic wrong."

Byrne accepted the praise, but told Fauntory, "I should warn the residents of D.C. that the people of New Jersey are not all that happy about taxation with representation."