A friend of mine who owns stock in the Standard Oil Company of Indiana found a letter from the company in her mail the other day. When she opened it, she extracted not a dividend check or a proxy form but a letter from the chairman of the board, John E. Swearingen, which she passed on to me. Addressed "to our stockholders," it was admirably direct:

"President Reagan has proposed to the Congress a comprehensive economic program involving substantial reductions in the federal budget coupled with tax cut proposals that are together designed to restore vitality to the nation's economy and to arrest inflation.

"The management of Standard Oil Company [Indiana] wholeheartedly endorses the president's program, and I am writing to urge our stockholders to express their support for it.

"While the president's party controls the United States Senate, the Democratic party is in the majority in the House of Representatives. Some congressmen have stated their opposition to the president's program and have been quoted in the press as saying that it will not pass."

Then Swearingen talked about the "failures of past programs" and the resulting damage to the economy, concluding that "the package President Reagan has proposed must be enacted, in its entirety, in order to reverse these trends and restore confidence in our economy and in our country.

"This may not happen," he warned, "unless the members of the House and Senate are reminded that Mr. Reagan's program represents the will of the people. I urge you, therefore, to write prompty to your representative and to your senators to express your support for his proposals. The future of our nation is at stake."

That sort of direct and dramatic pleading is rather unusual in a letter to stockholders. I do not recall an oil company president being quite so sure that the election represented "the will of the people" when the president was Jimmy Carter and the program involved a windfall profits tax. But the courts have upheld the use of corporate funds for the expression of opinions on referendums and legislative issues, and as a bit of a First Amendment fan myself, I have no desire to restrain Swearingen's freedom of expression.

Almost daily, the newspaper that pays my salary has its advertising revenues increased by full-page ads in which one corporation or another is telling Congress to quit dallying and pass the Reagan program. For not entirely unselfish reasons, I think that's a wonderful way to spend advertising dollars.

But if one has any sense of American history, one has to believe that both the corporations and the president whose program they are so enthusiastically promoting are on somewhat shaky ground.

Ronald Reagan came to the White House probably less beholden to big business than any other Republican president in this century. Big businessmen came rather late to his cause, and only after their original heartthrob, John B. Connally, had demonstrated he had less appeal in the polling places than in the board rooms. As a consequence, big business probably contributed less to Reagan's compaign than to any previous GOP nominee. And the votes that put Reagan in office obviously were not cast, for the most part, by the John Swearingens of this country.

But Reagan's budget and tax plans and his efforts to reduce government regulation of business have been embraced so passionately by corporate America that there is an almost automatic suspicion that the Reagan program may have been designed with big business in mind.

One has to wonder how helpful that will be to Reagan in the long run. Americans have learned to view skeptically the promises of big government, but that does not mean they are prepared automatically to accept political instruction from big business.

There is also a bit of a risk for business in this arrangment. Reagan's supply-side economics is a theory of uncertain validity. If its promise of abundance proves empty and produces only higher unemployment, deficits and inflation, then the adverse reaction could engulf not just Reagan and the Republicans but the business institutions that asserted that "the future of our nation" requires that the program be enacted "in its entirety."

But it may be that Swearingen is simply trying to revive the tradition of public persuasion that has been part of Standard Oilhs history since the days when that fabled public relations man, Ivy Lee, undertook to improve the image of its Rockefeller founders.

In the biography of the Rockefellers by Peter Collier and David Horowitz, Lee -- the ex-newspaperman who, among other things, suggested that John D. dramatize his philanthropies by handing out dimes -- is quoted as telling a group of executives: "Crowds are led by symbols and phrases. Success in dealing with crowds . . . rests upon the art of getting believed in. We know that Henry VIII by his obsequious deference to the forms of the law was able to get the people to believe in him so completely that he was able to do almost anything with them."

Perhaps the latter-day Standard Oil executives believe the same thing.