President Reagan's announcement that he will propose amendments to "put real teeth" in the 1968 Fair Housing Act is the opening salvo in a campaign by the administration to demonstrate that it is not dragging its feet on civil rights.

It is no coincidence that the amendments will be proposed Tuesday, the day before confirmation hearings are scheduled to begin on three controversial Reagan appointments to the U.S. Civil Rights Commission. "The president wants to make an advance on the fairness issue, and he wants to win approval of these nominations," White House communications director David R. Gergen said.

Nor is it any coincidence that the Justice Department at the same time is mounting a campaign, including an article by Attorney General William French Smith in this newspaper yesterday, to persuade Americans that it is enforcing civil rights laws vigorously. Smith referred in his article to the filing of three school desegregation suits as compared with two in the same period by the Carter administration. Other desegregation suits may be in the offing.

The new mood on civil rights in a White House becoming increasingly attuned to the 1984 presidential election reflects an understanding that there is a link in public perception between the issues of economic "unfairness" and administration insensitivity to minorities, particularly blacks.

Pollsters are telling the president that a majority of voters believe that his ad ministration is anti-poor, anti-black and anti-women. For a long time, the atti- tude of many Reaganites has been to minimize these perceptions or dismiss them as the political propaganda of the opposition.

Now, the prospect of sizable voting registration of blacks in southern states and increasingly militant criticism from women's groups has convinced Reagan's advisers that he must act visibly to change the public view that he is uncaring about minorities and women. Said one adviser, in a reference to civil rights: "It's like the environment. It's a settled issue on which most Americans expect a standard of performance from the president."

These advisers do not believe that Reagan is likely to rally many black voters to his banner. But they are convinced that he can assuage concerns of white moderates opposed to a presidential retreat on civil rights.

"It's very important that people think he's the president of the entire country," Gergen said. "It's important not just for political reasons but for his ability to govern."

President Reagan is soft-pedaling references to the Soviet Union as an "evil empire" these days, but he's still regaling audiences with anti-Soviet jokes, as he has for the past 30 years. Reagan's latest favorite, used at several recent speeches, concerns the commissar who went to a collective farm and asked a worker whether everything was all right.

"Certainly, sir," the worker replies. "I never hear a complaint."

The commissar, after more conversation, then asks the worker how the potato crop is faring.

"Potatoes?" the worker responds. "If we had piled them all up in one pile, they'd reach the foot of God."

"Just a minute," the commissar says. "This is the Soviet Union. There is no God."

And the worker responds: "That's all right. There are no potatoes, either."

Staff changes are continuing in the middle ranks of the White House. One of the next to leave, at the end of August, will be Aram Bakshian, who heads the speech writing team. He plans to write a political column for The Washington Times. So far, the White House has lined up no replacement.

Presidents are rarely asked about their sex lives, at least on the record, but Los Angeles Times reporter George Skelton didn't hesitate when the opportunity arose during a recent interview aboard Air Force One about Reagan's health and physical condition.

Skelton asked Reagan whether he had an active sex life, a question that provoked a memorable Reaganism.

"I better not answer because I remember the problems that Jimmy Carter had when he answered the question from Playhouse magazine," said Reagan, neatly disposing of the question, his predecessor and Playboy magazine in the same sentence.

The reference was to the 1976 Playboy interview in which Carter said he "looked on a lot of women with lust" and "committed adultery in my heart many times."

Reagan has made no such confessions. But he did share the following observations with an audience in Houston on April 29, during a discussion about the value of experience:

"And when you get along to where I am, you find out taking care of that personal machinery sure pays off when you get along to this stage, and you can still tie your own shoes and pull on your own socks without sitting down and do a lot of things that are much more enjoyable than that."