Tim Kraft, who stepped down a former president Carter's campaign manager Sept. 14 after allegations that he used cocaine, was cleared yesterday by a special federal prosecutor.

Prosecutor Gerald J. Gallinghouse of New Orleans informed U.S. District Court Judge Barrington D. Parker here that "the cumulative and credible evidence developed and presented" during FBI investigations "was not sufficient to overcome the legal presumption of innocence of criminal wrongdoing and to establish probable cause for any criminal charge against him."

Kraft, who now lives in Albuquerque, said through his lawyer, Thomas C. Green, "This nine-month exercise has been a tremendous cost to me personally and to the American taxpayer."

He said that defending oneself against "mischievous and meritless allegations" under the procedure required by the 1978 Ethics in Government Act is extremely expensive, and he called the act "an ill-advised law."

Kraft was appointments secretary to President Carter during Carter's first few years in the White House after playing a major role in Carter's 1976 campaign for president.

On Aug. 10, 1979, he was asked to manage the Carter reelection campaign, but he resigned Sept. 14, 1980, after published reports that a special prosecutor was being appointed under the terms of the 1978 law to investigate charges that he had used cocaine in New Orleans on or about Aug. 10, 1978.

Under the 1978 law, the attorney general is required to investigate and if need be appoint a special prosecutor whenever there are charges of criminal misconduct against ranking federal or campaign officials.

The allegations against Kraft reportedly stemmed from a White House aide who was testifying before a grand jury in a case involving allegations that Hamilton Jordan, Carter's White House chief of staff, had sniffed cocaine in New York in 1978. Jordan later was cleared by a grand jury.

Subsequently, a second allegation against Kraft, that he had used cocaine in California on Nov. 18, 1978, was placed under investigation.

At the time he quit as Carter's campaign manager, Kraft said, "I am completely innocent of the charges."

But he said, "I have not worked hard for President Carter for the past six years just to become a subject of political controversy in the final six weeks of his reelection campaign." Therefore, he said he would quit the campaign post to "avoid political exploitation of the false charges against me."

Robert S. Strauss, Carter's campaign chairman, said at that time that he expected Kraft to be vindicated.

Kraft, through his attorney, subsequently brought suit against the 1978 statute, asking that it be thrown out as unconstitutional.

The action formally clearing Kraft, 39, took the form of an order signed by Parker. The order, signed with the agreement of Kraft and his attorney, dismissed Kraft's suit against the 1978 law on the grounds that, since Kraft had been exonerated by the findings of the special prosecutor, he no longer has a cause of action.

Kraft, a native of Indiana, is a graduate of Dartmouth College and a former Peace Corps volunteer.