South African-born track star Zola Budd, in her most impressive victory of the season, won the women's mile at the Edinburgh Games yesterday despite swerving to avoid an anti-apartheid demonstrator.

Banners that read, "Edinburgh against apartheid" and "Zola Budd runs for apartheid," reportedly were erected by the Labor-controlled Edinburgh municipal authority. British television refused to televise the event live because of the banners.

During the race, which Budd won in 4 minutes 23.14 seconds to 4:27.97 for Irena Nikitini of the Soviet Union, a demonstrator carrying anti-apartheid leaflets ran on the track but was stopped before reaching Budd.

Budd said, "The demonstrator took me out of my rhythm and I had to take avoiding action, but it did not really upset me that much. People like that see me as a symbol of South Africa -- the best thing I can do is just keep on running.

"That was my best race of the season and the crowd were tremendous at the end. That's the best reception I've had."

Britain's Steve Cram, the world 1,500 meters record holder, won the 1,000 meters in 2:15.08, beating David Mack of the United States (2:16.90).

Steve Ovett of Britain held off U.S. runner Sydney Maree to win the men's mile in 3:55.01. Maree, closing at the tape, finished at 3:55.27. Other winners included U.S. triple jumper Willie Banks (55-4 1/4) and Soviet hammer thrower Yuri Sedykh (267-10). BOXING

Chris Schwenke, who underwent brain surgery after collapsing in the locker room shortly after a light heavyweight bout with Prince Mohammed of Ghana Monday at the Forum in Inglewood, Calif., responded to voice commands. But he was still listed in critical but stable condition after surgery to remove a clot on his brain.

Schwenke, 28, from Salt Lake City, was knocked out by Mohammed (32-1-2) with 18 seconds left in the scheduled 10-round bout. But he left the ring under his own power, Forum spokesman Blain Skinner said. About 20 minutes later, Schwenke (18-6-2) was talking with actor Burt Young and state Athletic Boxing Commissioner Marty Denkin when he complained of head problems and fell unconscious. FOOTBALL

Two homes belonging to Dallas Cowboys running back Tony Dorsett were seized by the Internal Revenue Service in an effort to collect more than $400,000 in income taxes, IRS spokeswoman Marlene Gaysek said. The homes in north Dallas and nearby Collin County could be sold within 30 days if the taxes allegedly owed for 1979, 1980 and 1983 are not satisfied, Gaysek told the Dallas Morning News.

In addition, he was named June 25 in a civil lawsuit filed by a local bank alleging he failed to pay a $175,000 unsecured note signed in March, the News said. Dorsett, 31, could not be reached for comment . . .

Former Pittsburgh Steelers running back Franco Harris has been hit with a tax lien of almost $48,000 by the IRS, according to court records. The taxes owed were for employes who worked for Harris and were not owed by the ex-Steeler himself. COLLEGES

Boston College basketball Coach Gary Williams will hold a news conference this morning to announce whether he will accept Wake Forest's offer to succeed Carl Tacy as coach, according to a Boston College spokesman.

While Williams, 39, refused to say which way he was leaning, he told the Boston Herald Wake Forest has "the resources that the Eastern schools don't have. They can do things that Eastern schools really can't do." Williams has a three-year mark of 63-30 at the Big East Conference school. JURISPRUDENCE

Richie Adams, the Washington Bullets' fourth-round pick in June's NBA draft who was arrested later that night in New York, appeared in Bronx Criminal Court yesterday, but had his case adjourned for the second time, according to Charisse Campbell of the Bronx district attorney's office.

Adams was arrested and arraigned on one felony count of criminal possession of stolen property and one count of unauthorized use of a vehicle. He is scheduled to appear Aug. 27. Campbell said the district attorney's office wanted more time to investigate. BASEBALL

Former Los Angeles Dodgers pitcher Steve Howe worked out for about 30 minutes Monday at the Metrodome for Minnesota Twins manager Ray Miller and President Howard Fox. Asked whether the Twins were impressed enough to consider obtaining Howe, Fox replied: "That's a good assumption." Howe has been treated twice for chemical dependency and was suspended for the 1984 season. He asked to be released by Los Angeles last month, but said his most recent problems, including a late arrival at one game and missing another, were not drug-related. HOCKEY

The St. Paul Pioneer Press Dispatch reported that independent Republican party leaders have asked Herb Brooks, fired by the NHL New York Rangers earlier this season, to consider a run for governor. BICYCLING

After 869 miles in the Race Across America (RAAM), distance cyclist Michael Secrest maintained a one-hour lead over professional racer Jonathan (Jock) Boyer, Michael Schermer and two-time RAAM winner Lon Haldeman.

The four front riders, setting a record pace in the 4-year-old cross-country race, reached Albuquerque in 53 hours. All three female entrants are still in the race, with Susan Notorangelo-Haldeman sixth overall among the 22 riders remaining.

If the present pace is maintained, the lead riders could be in Northern Virginia sometime Monday or late Sunday, race officials said.