THERE IS a tradition, called senatorial courtesy, that the Senate will not confirm a nominee from any state who is personally obnoxious to one of the senators from that state. It is an ancient tradition, justified on the ground that no one who is foolish enough to irritate a senator from his state is wise enough to hold an office important enough to require Senate confirmation. Circular at best, this logic can be carried to truly silly extremes.

Take the case of Adm. Elmo Zumwalt, the former chief of naval operations, who has been nominated by President Reagan and confirmed by the Senate as one of 14 appointees to the General Advisory Committee of the Arms Control and Disarmament Agency. Now the nomination is being sent back to the Senate by the administration at the behest of Sens. Harry Byrd Jr. and John Warner of Virginia, the admiral's home state.

No one disputes that Adm. Zumwalt is well qualified for the position: he has plenty of relevant experience and, though a Democrat, he endorsed President Reagan in 1980. But Adm. Zumwalt's home-state senators did not notice his nomination when it was approved unanimously in committee and on the floor (they complain that the White House failed to notify them), and now they want a chance to consider whether they will invoke senatorial courtesy.

One can understand their irritation. Adm. Zumwalt was the Democratic candidate against Sen. Byrd in the 1976 election, and no one likes opposition. The fact that the senator took little notice of the admiral in his campaign, and the large margin of his victory, suggest, however, that any wounds have healed. At least eight senators have supported the nominations of former opponents for various positions, and we would think Sen. Byrd, after examining the merits, would want to make a similar decision.

As for Sen. Warner, he was Navy secretary when Adm. Zumwalt was CNO; they disagreed on things then, later and now. Adm. Zumwalt in his book, "On Watch," called Mr. Warner a "dilettante" who suffered from a "chronic inability to make decisions." The senator says now that the Zumwalt nomination raises the question of whether one who writes a syndicated column, as the admiral does, should be in a position that gives him access to intelligence information, and he asks whether other syndicated columnists have served in such positions. The answer is that a number of members of such advisory boards are frequent contributors to different publications, and the issue properly before the Senate is whether the nominee has the qualifications and probity needed for the position. Adm. Zumwalt does. Sens. Byrd and Warner are entitled to be miffed at the White House's failure to notify them of his nomination. Having made their point, they should allow the nomination to be confirmed.