The Carter administration yesterday turned down Rhodesian Prime Minister Ian Smith's request to lay a wreath at the Tomb of the Unknowns in Arlington National Cemetery on the grounds that it would be a "partisan" attempt to influence U.S. policy.

Smith, who is scheduled to arrive in the Washington area today, had asked permission to lay the wreath at the outset of his controversial visit to seek American support for his transitional government in Rhodesia.

He and one of his three black partners in the transitional government, the Rev. Ndabaningii Sithole, are making the visit at the invitation of 27 senators. Their bid to Smith had touched off a major controversy about whether the U.S. government, which contends that the white minority-dominated Rhodesian regime is illegal, should give them visas to enter the United States.

Earlier this week, the administration, sensitive to charges that it favors radical guerrillas fighting the Smith government from bases outside Rhodesia, ended several days of indecision by granting the visas.

However, its action yesterday in barring the wreath-laying ceremony seems likely to touch off a new barage of charges by Smith's U.S. partisans that the administration's openly hostile to him and seeks to limit his movements in the United States.

The dicision to refuse permission for the ceremony was made officially by the Department of the Army, which has jurisdiction over military cemeteries. However, the State Department made known that it "is in accord with this decision."

In a statement explaining its action, the Army said the proposed ceremony "would plainly be an integral part of the overall purpose for Mr. Smith's visit, which is an attempt to influence U.S. policy. As such the wreath laying is considered 'partisan' in nature under Army regulations.

The statement added that Army regulations specify that "there must be no 'partisan' activity associated with the ceremony. A service is considered 'partisan' and therefore inappropriate if it includes commentary in support of or in opposition to or attempts to influences any current policy of the U.S. government."

Reliable sources said the State Department concurred because it felt the ceremony would have given the impression that Smith's visit had an official character. However, the sources added, the department does not feel that it is doing anything to impede Smith's movements or his access to the American public.

The sources also contended there is no inconsistency in the government denying permission for the ceremony while simultaneously making arrangements for Smith to meet with Secretary of State Cyrus R. Vance on Monday or Tuesday.

The Vance meeting, they said, will have apragmatic purpose - namely an attempt to convince Smith that the administration is not hostile to Rhodesia's whites and to urge him to accept U.S. and British calls for a conference of all the parties in the Rhodesia's conflict.

The United States consistently has argued that the best hope of preventing the guerrilla warfare from escalating into a bloody civil war would be through negotiaion of a cease-fire and a power-sharing agreement between Smith's regime and the guerrilla forces of the Patriotic Front.

So far, thought, Smith and the Patriotic Front's leaders, Joshua Nkomo and Robert Mugabe, have refused to deal with each other. In the meantime. Smith has moved ahead with his "internal settlement" plan for bringing about majority black rule in Rhodesia.

A strong core of sympathy for Smith has been evident in Congress; and, on his visit, he will be attempting to increase the support by pleading his case before the American press and a number of conservative political groups.

Upon his arrival today, Smith will go to Boston, Va., about 75 miles southwest of Washington, for a meeting with reporters and members of the American Security Council at the council's research institute.

The council describes itself as a nonprofit, nonpartisan private organization specializing in defense and security matters. However, it generally takes a conservative line favoring a strong national defense posture for the United States.