Gov. Thomas H. Kean signed into law yesterday a bill empowering the New Jersey Sports and Exposition Authority to build a stadium designed to lure a major league baseball team to the state and to acquire a race track to generate funds for the construction.

The governor said a New Jersey baseball team would not detract from the New York Mets or New York Yankees, but that a rivalry would increase attendance.

"We want to have a kind of ferryboat series," he said. "This is what we want. This is what we're going to get" . . .

Edward J. DeBartolo Sr.'s interest in buying the up-for-sale Pittsburgh Pirates has "probably" waned (says aide Paul Martha) now that the shopping mall magnate's defunct U.S. Football League team, the Maulers, is being sued by the Pittsburgh Stadium Authority for clearing out with three years left on a four-year lease . . .

Jim Finks, president and chief executive officer of the Chicago Cubs for just one year, in which he helped guide the club into postseason play for the first time since 1945, is stepping down.

Dallas Green, the Cubs' general manager, will assume the presidency Dec. 31, it was announced by the Tribune Co., which owns the National League team.

Finks, 57, resigned to pursue "other business interests," the club said. The former pro quarterback came to the Cubs after nine years as an executive of the NFL Chicago Bears . . .

The Atlanta Braves' third baseman, Bob Horner, had a 3 1/2-hour operation to repair his fractured right wrist and, while the surgeon, Peter Carter of Dallas, told the club it was a "complete success," he was hesitant to forecast how soon Horner may play. The team enthusiastically said he told them Horner would be "swinging a bat again in two to three months," but Carter amended, "I didn't say that. You can't say what might happen."

Horner has not played since he broke the wrist last May for the second time in less than a year. "When he got in there (to operate)," Carter's office said, "he saw that the fracture was not healed at all. He then . . . placed a screw into the bone. He was pleased with the results" . . .

Pitcher Britt Burns, who re-signed with the Chicago White Sox Monday for 1985 with an option through 1986, will be taking a pay cut of $75,000, to about $675,000. Burns, 4-12 in 1984 with a 5.00 ERA, said, "I know I don't deserve to be making so much money, and the club knows it."