Former Secretary of State Henry A. Kissinger has become the object of an increasingly bitter controversy on the campus of Columbia University, where a number of students and faculty are opposing his proposed appointment to a teaching post because of his "immoral" involvement in the Vietnam war.

Kissinger has not been formally offered the job, but is expected to tell university President William J. McGill before the end of the month whether he would accept a specially endowed chair in the political science department.

Already, however, opponents are comparing him to Nazi war criminal Adolf Eichmann and saying he is "unfit" or qualified only for a post in the "Department of Death."

Backers of the appointment see the issue in terms of academic freedom, and accuse opponents of trying to keep unpopular views off the campus.

Opponents of the appointment have held several rallies on the campus to denounce the offer, and the student newspaper, The Daily Spectator, said in a front-page editorial, "There is no place at Columbia for Henry Kissinger."

A faculty organization, complaining that university officials decided on the appointment in scret and violated normal review procedures, has obtained the signatures of over 130 faculty and research staff members to a letter opposing Kissinger; another group has prepared a petition signed by 1,000 students, faculty and staff members protesting the appointment. There are approximately 16,000 students at Columbia.

The opponents have offered a variety of reasons why Kissinger should not teach at Columbia, including the charge that the university is on a "celebrity hunt" and a contention that Kissinger's appeal to the university administration rests with his ability to raise money rather than with his credentials as a political scientist.

However, the thrust of the criticism has been against Kissinger's foreign policy role during the Nixon administration, and more particularly his participation in Vietnam war decisions.

"The violent, illegal and immoral policies of the Nixon administration in Vietnam, Cambodia, Laos and Chile must not be foregotten . . . A Columbia appointment would reward and legitimize Kissinger's policies. His actions have shown him unfit to teach here, and Columbia should not hire him," The Daily Spectator editorialized.

At a campus protest rally, 300 persons listened to Noam Chomsky, widely knows linguistics professor at the Massachusetts Institute of Technology, suggest sarcastically that if Kissinger is hired by Columbia, he should be appointed to "the Department of Death or of lies and Deception."

Chomsky, an outspoken Vietnam war critic, ridiculed Kissinger's academic qualifications, calling his essays a "parody of the academic style."

Kissinger, before being appointed national security adviser by Nixon in 1969, was a professor of government at Harvard University; he is now completing a six-month teaching appointment at Georgetown University in Washington.

Seymour Melman, Columbia professor of industrial engineering and a spokesman for the protesters, said in a telephone interview that university officials began trying to lure Kissinger to the campus without adhering to any of the many review procedures set up to guarantee faculty and student input into who is granted tenured teaching status.

Melman said that in a "rather cursory" department faculty meeting, the administration indicated that opponents to Kissinger would not be allowed to appear at an ad hoc review committee set up by the administration to consider tenured appointments, and that graduate students were not consulted about the appointment, as is normally done.

Instead, Melman said, the faculty group, was handed a one-page autobiographical sketch, and the matter was disinissed in one session. "It's unheard for such a thing to be carried off in one session," he added.

Melman also objected to "fundamental differences in values" between Kissinger and the faculty and student body, saying that Kissinger had violated international rules of war as Secretary of State.