President Reagan can quickly dispose of the controversy brewing over the Environmental Protection Agency. He can do so by cooperating with the US Congress in getting to the bottom of the charges now swirling around the agency, overhauling its management if necessary, and reassuring the American public that the agency will carry out its mandate - including the important one of cleaning up the nation's toxic waste dumps.
Of all the areas of government activity, protection of the environment logically should be one on which there is reasonable bipartisan agreement. Yet for two years the EPA seems to have generated nothing but confrontation. Now it is the target of accusations of political favoritism, personal squabbling, mismanagement, and coverups in the program to clean up hazardous waste. Mr. Rea-gan surely wants to avoid the political damage that might be done his administration by failure to put the agency in order and restore public confidence in it.
Anne Gorsuch, the feisty administrator of the EPA, did not help the agency's image when she refused to turn over subpoenaed documents to congressional committees. Congress cited her in contempt and a federal judge upheld the citation. Now she has further fueled public doubts by allowing the shredding of some official documents, said to be copies of the ones wanted by Congress - an act characteristic more of the Byzantine-like Watergate days than of an administration committed to forthright government.
The subject of the congressional investigation is a legitimate one. The House Energy and Commerce Committee and others are looking into the 1980 ''superfund'' law to see whether political considerations and favors to certain industries may have determined where and how millions of dollars have been spent to clean up toxic waste sites.
Mr. Reagan recently fired the head of the EPA program charged with this task, Rita Lavelle, and there appears to be some evidence that she was quarreling with EPA officials who wanted to crack down harder on polluting companies. One memo by her seemed to show that her administration was indeed partial to some industries as many environmentalists charge. Addressed to the White House, the memo criticized the EPA's chief counsel for ''systematically alienating the primary constituents of this administration, the business community.''
Embarrassing memos are not the issue, however. The public wants to know if the $1.6 billion fund to clean up hazardous wastes is being properly administered. How many of the 14,000 dumps nationwide have actually been cleaned up? (The EPA claims that about 110 sites have been given some federal aid; critics say that only a handful have received attention.) Are certain companies being favored because of their connections in the administration? Are private polluters being made to pay enough of the cleanup bill? How vigorously is the EPA carrying out this particular program? This may seem a peripheral issue to many Americans but certainly not to the hundreds of thousands of people who live near toxic dumps and chemical spills.
Now that Mr. Reagan has gotten involved in this matter, he presumably will want to do everything possible to help expedite the congressional inquiries, including turning over the needed documents. Standing on the so-called doctrine of ''executive privilege'' may have a certain appeal at the White House, but Mr. Reagan should know that it is a point of dispute among legal scholars and has yet to be resolved. By resisting congressional subpoenas, he will only feed public suspicion that the EPA has something to hide.
If the agency has not functioned well, moreover, the President should be the first to know this - and to want to do something about it. This, after all, is what effective leadership is all about.