USA Today, the Gannett Company's Rosslyn-based national newspaper, has signed on as an "official sponsor" of President Reagan's inauguration and given inaugural planners free space for full-page advertisements in its pages, inaugural officials said yesterday.

Several USA Today reporters, who asked to remain anonymous, and two authorities on journalistic ethics yesterday questioned the propriety of the arrangement, saying that there needs to be a clear separation between newspapers and government.

A USA Today spokesman said "the inauguration is not the government" and that "USA Today, as the nation's newspaper, is happy to be associated with positive, sometimes patriotic events that represent America at its best."

Asked if the advertisements were free, Charles Overby, communications vice president of Gannett, said: "I'm not going to go into how much we are charging. It is a special rate that is mutually satisfactory." Overby refused to elaborate on the ad rates.

Douglass Blaser, who handles marketing for the inaugural committee, said: "This is a donation of space. It's free. That's a special rate." Inaugural committee spokesman John Buckley said, "All the space is being donated."

Overby said the company approached the inaugural committee with the idea, and that he believes USA Today may be the first newspaper to sponsor an inauguration.

Overby, who was chairman of the Tennessee Republican Party in 1981, said that affiliation had nothing to do with the newspaper's sponsorship of the inauguration.

"It was the newspaper, not me," he said, adding that the GOP chairmanship was something he held "in my former life. . . . I was also editor of the Clarion-Ledger in Jackson, Miss., the paper that won the Pulitzer Prize for education reform."

Overby said the inauguration "is not a partisan event. Earlier this year we were dealing with Walter Mondale's people on things. That is my job, public affairs."

"USA Today is probably one of the most nonpartisan papers in the country," he said earlier, adding that the paper did not endorse a presidential candidate "for that very reason."

The cost of a full-page color advertisement, such as those the committee has run, is usually about $28,000, Overby said. The committee is expected to run 12 ads, worth about $336,000 in ad space, before the Jan. 21 inauguration.

Blaser said USA Today, which Overby said has a circulation of 1.3 million nationwide, is the perfect vehicle to make sure everyone in the country "had an opportunity to partake" in the celebration.

The advertisements, the first of which appeared Dec. 28, highlight the inaugural souvenirs, sales of which help defray the cost of the festivites and promote the event.

Yesterday, Richard M. Clurman, chairman of the Media and Society seminars run by Columbia University's graduate School of Journalism, said: "I do not think newspapers should be sponsoring events put on by governments, whether they are state, local or federal. . . . There needs to be a separation between government and journalism."

Clurman added that "every business has community responsibilities," including donating money to charity. But in the case of newspapers, these responsibilities "are better discharged not to government organizations," he said.

Gloria Cooper, Columbia Journalism Review managing editor, said, "My first reaction is to laugh. It seems to me the paper sort of put itself in the same league with M&Ms or Snickers, you know, like the official sponsors of the U.S. Olympics.

"A donation of such valuable space is bound to raise some questions about the newspaper's coziness with the administration and about its credibility."

Overby responded that the arrangement will not influence the paper's news coverage of the inauguration. "There is a separation of church and state here. There is nothing implicit or explicit about reporters writing favorable stories."

One reporter, who asked to remain anonymous, agreed that there "is a distinction between the business and editorial sides" of the newspaper. He said that no editor had ever suggested he write favorable stories on any subject.

But the reporter added that "there is a bit of distress and sadness among reporters that management does not have an awareness that you should distance yourself from the government."

Another reporter said, "I don't think it is the biggest ethical gaffe in history." He added, "It is no particular alliance with the Reagan administration. It is just this: 'We love the country, we love the flag, we love the White House, we love the Washington Monument' and they think it sells newspapers."

Overby said, "Certainly a presidential inauguration is pure Americana. It is that kind of Americana USA Today on a national basis seeks to have an identification with."