Rhodesian Prime Minister Ian Douglas Smith isn't the sort of person one expects to find starring in a Washington media event. He's an austere, even chilly man whose droning, British colonial speech, peppered with words like "bloke" and "mate," grates sharply on American ears.

Yet, for the past week, Smith's daily dawn-to-mignight whirl of public appearances and press interviews has made him a lightning rod for attention.

Wherever he's gone. Smith has had what seems like a permanent supporting cast: a phalanx of police and plainclothes bodyguards, a trailing army of reporters and television camera crews and, in the background, a chorus of demonstrators chanting such taunts as "Hitler rose, Hitler fell! Ian Smith go to hell."

The attention derives from what Smith calls his status as an "outlaw" - the man who 13 years ago led Rhodesia's white minority to break with British rule and who since has defied the combined efforts of black Africa and the western powers to bring him to heel.

Now, Smith is midway through a campaign, at once audacious and desperate, to appeal to and over the head of the Carter administration for American support of his plan to move Rhodesia, a country of 250,000 whites and almost 6 million blacks, to majority black rule.

To do that, SMith has unleashed a lobbying and media blitz whose intensity was made doubly remarkable by the fact that it's been a one-man show. But, as Smith now moves into the second half of the U.S. trip, campaign to California and Texas, a big question remains about what, if anything, he has accomplished.

He did strike some isolated sparks of success, most notably in getting former Secretary of state Henry A. Kissinger to say the United States should at least give Smith the chance to go ahead with his so-called "internal settlement" plan for Rhodesia as a means of testing his good faith.

For Smith, that alone probably was worth the price of his trip because it made Kissinger the first person of commanding stature in U.S. Foreign policy circles to say anything sympathetic about Smith's government.

On Capitol Hill, where Smith always has had a hard core of conservative sympathy, he failed to make any real headway in broadening his base. Still, he did coax some wary senators into saying they would take a new, open-minded look at Smith's progress in making good on his pledge to bring about democratic majority rule.

Despite these scattered successes though, even some members of Smith's entourage privately admit that, when the effort is viewed on terms of overall impact, he didn't get his message across as strongly as he had hoped.

In particular, the goal that Smith candidly said was his No. 1 priority - winning the Carter administration's support - remained beyond his grasp. In fact, the administration, which reluctantly allowed his visit only because of charges that it was suppressing unpopular views, carefully kept him at arm's length.

The administration consistently has said that Smith's biracial transitional government - one that involves his sharing power with three black leaders while preparing the country for majority rule elections - cannot, by itself, bring about a peaceful resolution of the Rhodesia problem.

Washington's principal objection is that the Smith government lacks the support and participation of the Patriotic Front guerrilla forces fighting it from bases outside the country. As a result, the administration believes that a successful solution requires Smith and the front leaders to negotiate a power-sharing arrangement - something that both sides so far have refused to do.

That administration remains adamant on that point was made clear to Smith when he met with Secretary of State Cyrus R. Vance. When Smith then asked for the chance to press his case personally with President Carter, the president seized the opportunity of a nationally televised press conference to say that, as long as Smith held to his present course, there would be no point in such a meeting.

Smith encountered a similiar frustration in his efforts to outflank the administration by carrying his arguments to the American public. Smith admits that the U.S. press gave him and his three black colleagues an almost unprecedented opportunity - through newspaper and TV coverage and through meetings with influential media executives - to tell their story.

But, some of his aides say privately, the available evidence doesn't leave them much reason for optimism. The press, judging by the tone of most editorial comment on Smith's trip, seemed to be unconvinced; and the public, apparently because of Rhodesia's distance from the concerns of the average American, seemed disinterested.

As a result, Smith spent much of his time preaching to the already committed. His speeches, while generally well-attended and applauded, usually were before conservative audiences and organizations that already regard Rhodesia as an anticommunist bulwark amid the instability of Africa.

In addition, Smith suffered from some unavoidable accidents of bad timing. He came to the United States at the invitation of 27 senators, but he arrived in the midst of Congress' last-minute rush to adjourn and found that even many of his hosts didn't have much time for him.

When the principal sponsor of Smith's trip, Sen. S. I. Hayakawa (R-Calif.), kicked off the week by arranging a meeting on Capitol Hill, only about 10 senators showed up. Through sheer persistence in the ensuing days, Smith did get to talk to several more members of Congress; but, as one Senate aide noted, "This was a week when Rhodesia wasn't exactly at the top of anybody's list of priorities in Congress."

Finally, Smith wasn't exactly helped by the unfolding of events back in Rhodesia. During the week, his government in Salisbury announced the ending of Rhodesia's racial discrimination laws; but instead of winning applause the move caused a barrage of charges that the easing of restrictions was really a sham and cynical attempt to win sympathy for Smith while he was in the United States.

By yesterday, the news dispatches from Rhodesia were telling a different and darker story - that police had shot and killed five blacks, including a baby, while searching for guerrillas.

The results was to see Smith leaving the East Coast for California as his critics were charging that the latest killings said more about the nature of his government than all the arguments and explanations he had made here.

As Sen. Edward M. Kennedy (D-Mass.) told the Senate yesterday: "If Mr. Smith takes back any message from America, let it be that the path to peace and stability in Rhodesia cannot be obtain through obduracy . . . I do not believe the Carter administration should or will endorse his solution to halting the turmoil in Rhodesia."