Washington ballet-goers are in for a special treat when the American Ballet Theatre is here next month: Mikhail Baryshnikov will be dancing five performances during the first two weeks and is expected to dance two more the final week. Baryshnikov will dance "Giselle" on opening night April 2 and again on April 4. All the ABT performances of "Giselle" throughout this tour have been underwritten by Washington lawyer Mike Feldman as a fifth-anniversary present for his wife Adrienne Arsht Feldman.

On the ABT Gala Evening April 8, Baryshnikov will dance Act 2 from "Swan Lake" with Bonnie Moore, another rising star from Mary Day's Washington School of the Ballet. She left the Washington Ballet in 1984 and joined ABT that fall. Baryshnikov will also dance an all-Tchaikovsky evening April 9 and the world premiere of a new Karole Armitage ballet April 10. The "Giselle" ballet will be the theme of the Giselle Ball, a black-tie fundraiser April 14 in the new Westin Hotel. The Question of Mrs. Ortega's Visa

How tough is President Reagan really getting with Nicaragua? Nicaraguan First Lady Rosario Murillo de Ortega has canceled a trip to the United States, which would have included attending a drug prevention conference tomorrow in Atlanta where Nancy Reagan will speak. According to the Nicaraguan Embassy, the cancellation is because the State Department refused to issue her a visa. Embassy spokesman Sarali Porta said Murillo was to have left for the United States Tuesday, but as of late that evening the U.S. Embassy in Managua had not given her a visa. Murillo had planned to travel to New York, Washington and other cities following the drug conference.

The State Department denies that a visa was refused. Bruce Hammerman, a State Department spokesman, said, "Our embassy in Managua was instructed to issue the visa as soon as the Nicaraguan Foreign Ministry submitted her flight itinerary, which, since Ms. Murillo is the wife of a head of state, is needed for security and protocol reasons. The Nicaraguan government is well aware of this requirement."

Nicaraguan Embassy press spokesman Miriam Hooker said the State Department received the scheduling information for the trip March 13 and that they had been waiting for the visa ever since. Murillo, she added, returned to Managua from the funeral of Olof Palme in Sweden on Tuesday with a bad cold. Because of that, she decided not to attend the drug conference but did plan to continue her visit to the United States for speaking engagements through April 1. End Notes

There's going to be a great shuffling around at the coveted head table of this weekend's Gridiron Dinner since the dean of the Washington diplomatic corps, Anatoliy Dobrynin, will not be able to attend. The Soviet ambassador still has not returned to Washington from the Soviet Communist Party conference in Moscow two weeks ago when he was elevated to the Secretariat of the party's Central Committee, which will require him to return home after 24 years in Washington. An embassy spokesman would not say when Dobrynin would return to Washington for a host of farewell parties, but said he should be back by April 1. Dobrynin had accepted the invitation of the Los Angeles Times to attend the Gridiron. According to the embassy, he has missed only three of the dinners since serving in Washington . . .

The music men were on Capitol Hill yesterday singing against a piece of proposed legislation that hits their pocketbooks. Singer-songwriter Donna Summer spoke before the Congressional Black Caucus, Sens. Ted Kennedy and Howard Metzenbaum and other members of Congress about the proposal that would reduce royalty payments for songwriters on syndicated local television shows. Grammy award-winner Lee Greenwood performed before the Congressional Rural Caucus late yesterday as part of the lobbying effort and songwriters Marvin Hamlisch and Marilyn Bergman were also making the rounds on the Hill . . .

Amy Carter and 13 other college students were arrested yesterday in a protest at an IBM office in Providence, R.I. The students were demonstrating against IBM's business dealings in South Africa. The Brown University freshman was also arrested in a protest last April at the South African Embassy here . . .

After 11 days of seclusion in a hotel in Limerick, the Bhagwan Shree Rajneesh left Ireland Tuesday with a party of 13 in a twin-engine jet. He was en route to Uruguay. After being kicked out of country after country and refused entry by others, he'll probably find a home there. Uruguay has a history of accepting undesirables . . .