Jordan details White House agony over Iran hostage crisis; Crisis: The Last Year of the Carter Presidency, by Hamilton Jordan. New York: G. P. Putnam's Sons. 431 pp. $16.95.

One gingerly approaches the political memoirs of a man who was generally regarded as the enfant terrible of the Carter administration.

The name Hamilton Jordan recalls images of a brash Georgian whose Washington antics were a frequent source of embarrassment to the 39th President of the United States. Yet Jordan's account of Mr. Carter's troubled last year in office omits the rationalizations that one might expect from the former White House chief of staff.

Instead, the author correctly contends that, from the seizure of the United States Embassy in Tehran Nov. 4, 1979, until the presidential election a year later, the Carter administration was no less a captive than were the 53 American hostages.

It was an agonizing time for the nation, and Jordan's crisp narrative provides a personal perspective that is at once credible and compassionate.

He matter of factly recounts the process by which he found himself drawn into the eye of the storm. It began in December 1979, when the President sent Jordan to Panama to see if General Torrijos would take the Shah of Iran off Washington's hands. These arrangements included an anxious audience with the deposed monarch to convince him that his leaving the US would improve President Carter's chances of freeing the hostages.

Shortly thereafter, Jordan was summoned to a secret Florida rendezvous, where he was informed that a French lawyer and an Argentinian businessman with Iranian contacts were interested in starting secret negotiations between the US and Iran. They selected Jordan because he was the President's confidant, yet he wasn't connected with the State Department.

President Carter's reluctance to cast his chief of staff in the role of a secret negotiator was soon overcome by the absence of available options. Thus, for the next four months, the author was assigned the delicate diplomatic mission of opening the lines of communication between Washington and Tehran.

In the course of his clandestine assignment, Jordan made numerous transatlantic flights, assumed an alias, and was even provided with a disguise by the CIA. He also met with an Iranian official who calmly informed him that the hostage crisis could be concluded once the CIA assassinated the Shah. The official isn't identified in the book, but Jordan recently revealed it was the late Iranian Foreign Minister, Sadegh Ghotbzadeh.

As the months dragged on, with conflicting signals coming from Tehran, President Carter became convinced that the Ayatollah's aim was to humiliate the US. Consequently, he canceled Jordan's diplomatic role and chose the military option.

One of the book's most compelling sections recounts the briefing that the President and his staff received from Col. Charlie Beckwith, who commanded the rescue mission.

One senses the tension that existed in the White House ''Situation Room'' as the President's men charted this perilous course. And when the mission aborted, the reader shares President Carter's anguish at having to announce that eight men died in the ill-fated rescue attempt.

Following the failure of ''Desert 1,'' President Carter ended his self-imposed ban on political campaigning, and Jordan devoted his energies to the reelection campaign. The remainder of the story is well-known, and Jordan summarizes the electoral ambush that awaited the beleaguered President. He then concludes with a moving account of Mr. Carter's departure from Washington and his subsequent meeting with the freed hostages in Germany.

The book's diary format provides an immediacy that is often lacking in political retrospectives. Yet the effect can be distracting, especially when the author interjects personal asides that interrupt the narrative.

A case in point is Jordan's legal travail concerning his alleged cocaine possession. Granted, the case had a bearing on the hostage crisis insofar as the defendant was the President's secret emissary. Yet the author's personal problems seem incidental to the diplomatic mission with which he was entrusted.

Equally grating is Jordan's use of trite expressions such as we ''cleaned Kennedy's clock'' or they ''ripped the Shah off.''

But these flaws are clearly overshadowed by the book's many merits - most notably the author's candor in conceding his several limitations.