The Defense Department bade farewell to Gen. Alexander M. Haig yeesterday, awarding the onetime White House chief of staff and NATO commander four Distinguished Service Medals in a parade-ground ceremony at Fort Myer.

Defense Secretary Harold Brown, presenting one of the medals, hailed the retired general as "the complete professional through his distinctive military career."

Haig officially wound up his 31 years of active-duty Army service on Saturday when he retired as Supreme Allied Commander in Europe. From May 1973 until August 1974, the darkest days of the Watergate scandal, he was President Nixon's chief of staff.

Haig's Watergate connection, according to some political operatives, could cloud any ambition to hold public office that the general may pursue in his new role as private citizen.

The 54-year-old Haig spoke light-heartedly yesterday about speculation he will go into politics. Haig told the crowd of well-wishers gathered yesterday on a sunny hillside at Fort Meyer that after he escaped an assassination attempt at Obourg, Belgium, last week, former secretary of state Henry A. Kissinger called him and said: "'Al, now I know you're a political candidate.'"

Haig said he also received a call from Brown in which the defense secretary said, "'Al, I just called to inform you that we didn't do it.'"

The general said Monday's "sudden groundswell" was not the kind he had in mind as he looked to his future potential as a political candidate.

Asked at the reception following the awards ceremony whether he would run for the Republican Senate seat being vacated by Pennsylvania Sen. Richard S. Schweiker, Haig replied: "no, no."

Pressed to specify his plans, Haaig said: "I don't discount anything. You never know what you might find under a rock."

Haig, who has rented a home in Philadelphia, has been booked for a heavy schedule of speeches and meetings, including sessions with Chase Manhattan Bank, International Investors Conference, International Council of the Aerospace Industries Association and Executives Club of Chicago.

One Haig confidant said yesterday that the general's immediate plan is "to make some money," presumably by taking a high-paying job in an industry with international interests. In such a post, he could wait for political lightning to strike.

Onr gotmrt executive at the Republican National Committee said that Haig has "no ready-made constituency" to boost him over other political hopefuls.

In the serious part of his farewell speech yesterday, Haig repeated his charge that the Soviet Union is partly responsible for the "global disease of terrorism."

Haig's official send-off from the Pentagon included receiving the Distinguished Service Medals of the Army, Navy, Air Force and Defense Department. Military leaders seem to agree that Haig did an outstanding job as NATO commander, shoring up the alliance through a combination of toughness and diplomacy.

Haig rose from modest beginnings to fill some of the Army's top jobs. Some Nixon administration executives credit Haig with running the country in the fragile period when Nixon was hesitating over resigning.

Speaking of the four medals awarded to him yesterday, Haig said they were "proof positive" that the U.S. system of government "is an extraordinary system for very ordinary people." CAPTION: Picture, Secretary of Defense Harold Brown pins one of four Distinguished Service Medals on Gen. Alexander M. Haig. UPI