In the first full-blown Republican assault on the Carter administration's foreign policy, President Carter yesterday was excoriated for "compromising America's ability to defend itself" and bumbling leadership of the Western world.

A political indictment issued in the name of all 38 Republicans in the Senate charged that:

"In 15 short months of incoherence, inconsistency and ineptitude, our foreign policy and national security objectives are confused and we are being challenged around the globe by Soviet arrogance."

A 29-page catechism of fault-finding on U.S. defense and diplomatic posture, which amounts to a scene-setter for this year's congressional election campaign, was made public at a Republican leadership press conference on Capitol Hill.

Sen. John G. Tower (R-Tex.), chairman of the Senate Republican Policy Committee, which Coordinated the critique, Senate Minority Leader Howard H. Baker Jr. (R-Tenn.) and Sen. Carl T. Curtis (R-Neb.), chairman of the Senate GOP Conference, couched their chorus of criticism in more-in-sorrow-than-in-anger tones.

In "the bipartisan spirit" that has characterized American foreign policy "since World War II," Tower said, reading the introduction to the indictment, the minority party "should not engage in needless partisan carping" or political exploitation of great world issues. But "having acted with restraint" until now, he said, it would be "a dereliction of duty" to stand silent in the face of the Carter administretion's transgressions.

The central thrust of the broadside was that Senate Republicans cannot "remain silent while an inexperienced and inept leadership is compromising America's ability to defend itself" and engaging in "patterns of conduct," especially with the Soviet Union, "tht if continued, could lead to disaster."

The first snap reaction by an administration official came from State Department press spokesman Hodding Carter, who said:

"I don't have an official response to that except to note that, first, we clearly do not believe that our policy has that effect or has that intent." Secondly, Carter drily added, "I would note that the purpose of the opposition is to oppose, and such resolutions (sic) I don't find particularly surprising - nor do I think they are particularly edifying."

The GOP critique and remarks of the three senators showed that they see as an especially tempting political target the drawn-out negotiations now approaching a conclusion in the American-Soviet nuclear strategic arms limitation talks (SALT).

Tower said: "I would think that a substantial majority of the Armed Services Committee would not be able to accept the SALT treaty as we see it trending now" and "this is a matter on shich [Senate] feelings I think will run much deeper than they did even on the Panama Canal treaties . . ."

Baker said he had just returned after serving as an observer at the American-Soviet SALT negotiations in Geneva, and sees "a fair chance that some sort of treaty will be signed" this summer, probably at a washington summit conference between Carter and Soviet leader Leonid I. Brezhnev.

"There's nothing wrong with that, provided it is a good treaty," Baker said, and that is what troubles him. (The State Department said yesterday there is "no plan for a summer summit" - but did not rule that out.)

What is significant about tha alarm sounded yesterday, Curtis and his fellow senators said, is that "this document was approved unanimously by all the Republican U.S. senators," across the liberal-conservative spectrum.

Among other things, it said, "We believe the Carter administration incorrectly interprets the intentions of the Soviet Union and its commitment to achieve conventional military and nuclear superiority to secure wide-ranging, geopolitical goals." The administration was charged with failing "to understand adequately and communicate to the American people the nature of the Soviet threat."

"It is evident that no one, including the president, is in control of the foreign policy process," the Republicans charged. The president, personally, was charged, in part, with commenting "impulsively on critical foreign policy positions" producing a policy that is "a patchwork quilt without continuity . . . frequently charged at a whim with a glaring absesence of toughness and firmness."

Around the administration was accused of:" Freckless handling of the Ethopian-Somalia conflict [that] opened the way for the Soviets to carry out their naked geopolitical power play" in the Horn of Africa.

Producing a "failure of Middle East policy . . . largely attributable to a seemingly never ending series of gaffes, miscalculations, imprecisions, indecisions and indiscretions of word and action."

". . . Placating [in Africa] the most militant common denominator in disputes such as Zimbabwe [Rhodesia] and Namibia [Southwest Africa]" rather than "letting the moderates work out a solution themselves."

Following, in nuclear negotiations, "a frightening pattern of giving up key U.S. weapons systems for nothing in return"; permitting "glaring deficiencies in NATO's defenses"; "timidly" failing to resist the "growing influence of Eurocommunism," and also widening the risk that America's European allies may feel compelled "to go their own way in defense" and even make "unilateral accommodations with Moscow."