The Senate broke a 37-year deadlock yesterday and voted 83 to 11 to ratify an international treaty outlawing genocide that has been endorsed by six of the last seven presidents and approved by 96 other nations.

"We have waited long enough," said Senate Majority Leader Robert J. Dole (R-Kan.), adding: "As a nation which enshrines human dignity and freedom as a God-given right in its Constitution, we must correct our anomalous position on this basic rights issue."

The Senate approved the U.N. pact with several reservations, including one that allows the United States to exempt itself from the jurisdiction of the International Court of Justice (World Court) in cases stemming from the treaty.

But it voted 62 to 31 to reject a proposal by Sen. Steve Symms (R-Idaho), dubbed a "killer" amendment by treaty supporters, that would have unilaterally rewritten the treaty's terms to bar deliberate annihilation of political as well as racial and other groups.

In order to accomplish the same purpose without jeopardizing U.S. ratification of the treaty, the Senate then voted 93 to 1 to direct President Reagan to attempt to negotiate the change after ratification, as Reagan has indicated he is prepared to do.

Even its strongest advocates concede that the treaty is largely symbolic, especially in light of the World Court exclusion, which other countries, including the Soviet Union, have also claimed. But Jewish and other groups hailed the accord and the Senate's ratification of it as an important commitment to combat genocide -- an "overwhelming bipartisan expression of the best instincts of the American people," said Nathan Perlmutter, national director of the Anti-Defamation League of B'nai B'rith.

The treaty, officially called the International Convention on the Prevention and Punishment of the Crime of Genocide, was drafted in the aftermath of Nazi extermination of European Jews. It was signed by the United States in 1948 and submitted to the Senate in 1949.

It declares genocide to be an international crime to be prevented and punished. It defines genocide as killing, inflicting serious bodily or mental harm, imposing conditions designed to destroy, preventing births and forcibly transferring children of any national, ethnical, racial or religious group.

While it was endorsed by all postwar presidents except Dwight D. Eisenhower, it ran afoul of conservative objections that it threatened U.S. sovereignty and constitutional protections.

Senators yesterday attributed the treaty's eventual success to a variety of factors, including a 1976 switch from opposition to support by the American Bar Association, Reagan's endorsement of the pact in 1984, Dole's leadership, and negotiations between Foreign Relations Committee Chairman Richard G. Lugar (R-Ind.) and a treaty foe, Sen. Jesse Helms (R-N.C.), on the World Court and other reservations. Another factor frequently cited yesterday was the long, often lonely crusade on the treaty's behalf by Sen. William Proxmire (D-Wis.), who took the floor every day the Senate was in session since Jan. 11, 1967 -- about 3,000 times in all -- to advocate ratification.

"We're all very grateful to you," Sen. Howard M. Metzenbaum (D-Ohio) told Proxmire in one of several tributes that transcended partisanship. Proxmire credited Reagan's support as critical.

Most of the objections raised in the final two days of debate centered on the exclusion of political groups from the list of those to be protected under anti-genocide rules. Persecution over the years has shifted from racial and religious groups to political minorities, Symms argued.

After defeat of his amendment, Symms voted against ratification of the treaty, as did Helms and Republican Sens. Jeremiah Denton (Ala.), John P. East (N.C.), Jake Garn (Utah), Barry Goldwater (Ariz.), Charles E. Grassley (Iowa), James A. McClure (Idaho), William V. Roth (Del.), Strom Thurmond (S.C.) and Malcolm Wallop (Wyo.).

Only Goldwater voted against the resolution urging the post-ratification addition of an amendment barring genocide against political groups.