"I would like to be famous one day a month," the author of "Roots" said yesterday.

It came late on a Saturday afternoon, in a whirlwind week during which Alex Haley returned from a trip to Africa, received a special Pulitzer prize, was sued for plagiarism, received his 12th honorary degree, and still had one of three speeches to make.

In conferring an honorary doctorate of humane letters on Alexander Palmer Haley yesterday, American University President Joseph J. Sisco observed: "Few people have succeeded, as you have, in capturing the attention of Americans."

In a few moments away from autograph-seekers and hand-shakers, Haley yesterday admitted, with a touch of wistfulness, that he does sometimes miss the quiet hours of research - "months of 12 hours a day spent with old documents" - in the midst of the maelstrom of public attention of today.

"It was just like getting snatched off the ground. I have the feeling that I want sometimes to get my feet back to earth and get back to the typewriter. I love being alone and a typewriter . . . I love and respect the craft of writing. I just can't do it now that I am out speaking. Soon I've just got to get out of this."

Haley's next project is a book called "Research," which will detail the 12 years of research that he put into "Roots," which has become a bestseller, a TV series that drew the largest audience ever, a kind of popular folk epic and a social phenomenon.

Haley is a quiet man, and the white hood of the doctorate of humane letters falls quiet naturally from his shoulders. He speaks in studied statements - particularly when asked about the recent suit against him by Margaret Walker Alexander, who has claimed that sections of "Roots" were copied from her 1966 novel, "Jubilee."

Haley, pointing out that the case was now in litigation, declined specifically to answer the charges but did repeat that he does not recall having read "Jubilee" which Alexander wrote under the name Margaret Walker.

"I think that with great success, sniping and attacks seem to go with the territory," the author of "Roots" said yesterday.

He recalled that he once spoke at Jackson State College when Alexander was head of the program and that "she said some nice things about me and I said some nice things about her." As for her novel, "Jubilee," Haley said that he was away of it as anyone would be who was familiar with the literature and studies of the black experience.

Then there was also another claim from Harold Courlander, of Bethesda, a retired Voice of America employee and a collector of African oral folk tales. Courlander, who published a novel titled, "The African" in 1967 told a reporter that he had felt a "sense of deja vu" while reading "Roots." He has compiled a list of sections that he claims show similarities between the two books.

"I don't recall ever coming acros it "(The African")," Haley said yesterday, and then added with a bit of a bite: "It is beginning to sound as if I went around finding various books to copy. It wouldn't take me 12 years to copy. I spent 12 years in research. It wouldn't take me 12 years to copy. I type faster than that."

Another controversy swirling around "Roots" has been the criticism from Mark Ottaway, a reports for the Sunday Times of London, who has raised factual questions about the African portion of Haley's book. Yesterday Haley pointed to the defense by Gambian official of the griot, the oral tribal historian, whose professionalism was questioned by Ottaway.

"I never once called my book a history," Haley observes. "I called it a symbolic symbol of a people and it just happened to be the story of my family."

Being a celebrity does have its compensations, however, as Haley found out yesterday. One of the American University professors who received a teaching award came up to shake his hand and said: "In one week you educated more American people than any of us."

Haley shared the honorary degree awards yesterday with Kurt Waldheim, secretary general of the United Nations, and Robert E. Cleary, former president of American University, both of whom received honorary doctorates of law.

Although Waldheim noted that it was far too early to judge the effects of the policy of the new administration of President Carter, he said that there has been "a refreshing sense of purpose and of determination to take a new look at some of the oldest and most difficult of the world's problems."