It's not easy to tell what food is fit for a queen, but cooked rodents apparently qualify. Queen Elizabeth dined Thursday night on roast gibnut, a rodent similar to a rat, during her stay in Belmopan, Belize.

Wire services report that the queen "picked" at the delicacy, but perhaps because she had eaten a four-course lunch prepared single-handedly by Olga Arnold, 53, who lives in a poor area of Belize City.

Arnold wound up doing the cooking because, she explained, "I'm sort of well known around here. When people hear of something like this, they usually say, 'Well, let's get Olga, she can do a good job.' "

The queen sampled Arnold's shrimp remoulade, roast beef with stuffed tomato, water lilies and fruit cocktail, but the cook and the queen did not meet.

Earlier this week the queen received the key to Belize City from the mayor while sitting on a makeshift throne erected atop a concrete traffic divider in the middle of an intersection. This was her first stop in a 26-day tour of the Caribbean. Belushi Tape Played

On a tape played in a Los Angeles court yesterday, Cathy Evelyn Smith said she bought comedian John Belushi heroin and injected him with the drug several times in the last 24 hours of his life, calling his death "all my fault."

Sounding somber and depressed in the tape of a telephone interview, Smith, 38, a former rock backup singer from Toronto, expressed both affection for the comedian and guilt over his drug overdose death. The interview was conducted by Los Angeles free-lance writer Christopher Van Ness shortly after Belushi's death in March 1982.

Prosecutors consider the tape a key piece of evidence against Smith, who returned from Canada to Los Angeles earlier this year to face a second-degree murder charge and 13 counts of administering combinations of heroin and cocaine, or "speedballs," to Belushi. Her preliminary hearing in Municipal Court will determine whether she should stand trial.

Following a prolonged battle to keep the tape confidential, Van Ness turned it over to the court Thursday after he was ordered to serve a 10-day jail sentence for contempt of court. He was freed from custody after agreeing to hand over the tape. End Notes

Vice President George Bush caused a stir last week when he dropped by Baptist Hospital in Columbia, S.C., to visit Lee Atwater, President Reagan's former deputy campaign manager, his wife Sally and their newborn son Ashley Page. A large crowd gathered to witness the surprise VIP visit, but according to a spokesperson at the hospital the gawkers kept their distance and "were very well-mannered." Doctors posed for pictures with the vice president, Atwater said. "That's a big event in Columbia, S.C.," he said . . .

Sly Sighting: Once again Sylvester Stallone has been seen around town. Earlier this week he was spotted at a downtown Nautilus Fitness Center, working out with two friends. When recognized, the actor signed autographs for his body-buildingfans . . .

American millionaire John Paul Getty II has donated $700,000 for the expansion of the Imperial War Museum in London, museum officials said yesterday. The reclusive Getty, who lives in London, has become a patron of arts and sports in Britain, giving millions of dollars for redevelopment this year . . .

At a fashion show at the Vista International Hotel yesterday, a model named Gardenia lost the shirt off her back. During the show, which featured New York designer Frank Composto's fall collection, Gardenia modeled a beaded evening dress and the strapless top slid down in front of a crowd of 400. She reportedly pulled up the top and continued . . .

Chris Downey, wife of Rep. Thomas Downey (D-N.Y.), plans to open a Capitol Hill pizzeria later this month, serving -- what else? -- New York-style pies, a spokesman for the congressman confirmed yesterday. She'll call it Prima Pizza.