Former secretary of defense Caspar W. Weinberger is joining the law firm of Rogers & Wells as a Washington-based specialist in international law and finance, the firm announced yesterday.

The 275-lawyer firm is headed by former secretary of state William P. Rogers. The announcement, issued by Rogers & Wells' New York headquarters, said Weinberger "will not engage in any work involving federal government or defense contracts or any matters involving the Defense Department in any way."

Weinberger was also recently appointed to the National Economic Commission that will look into federal budgets and deficits.A Monetarist's Medal? . . .

A new "trophy" is sitting on the breakfront in the office of Beryl W. Sprinkel, chairman of the Council of Economic Advisers. The trophy, which rests next to a plate presented by the prime minister of Japan, is a gift from Sprinkel's friend James C. Miller III, director of the Office of Management and Budget.

Miller, it seems, decided Sprinkel needed cheering up because The Wall Street Journal had blasted him in a recent editorial. The Journal, in the spirit of the Olympics, was awarding medals to recent economic pronouncements, and declared that the annual economic report written by Sprinkel deserved a lesser prize than the encyclical issued by Pope John Paul II. (The Journal favors a gold standard; Sprinkel is a monetarist who pays close attention to fluctuations in the money supply.)

"Lest we insult past winners of the bronze," The Journal said, "Beryl Sprinkel's medal will be fashioned from Styrofoam."

So Miller, who shares Sprinkel's views, decided to present him with a mock medal. The budget director cut out the bottom of a Styrofoam cup, wrote "WSJ" on it, threaded a gold ribbon through it and placed it lovingly on a bed of pink tissue in a fast-food hamburger container. Sprinkel, delighted, sent Miller a letter expressing his "enormous gratitude for the prestigious award."

Those monetarists are such a madcap bunch . . . . Headed for Hudson . . .

Indianapolis bound: George A. Keyworth, former White House science adviser and advocate of the "Star Wars" spaced-based missile defense program. The Hudson Institute, a public policy analysis and research organization, is expected to announce his appointment March 10 as its director of research.

Keyworth, who has operated a consulting firm here since January 1986, will join another old Reagan hand, Mitchell E. Daniels Jr., at the institute. Daniels, a former White House political director, joined Hudson in February 1987 as the group's president and chief executive officer.