Andrei Ustinov, a Soviet dancer who left the Moscow Ballet last week during the Dallas stop of its U.S. tour, has been granted political asylum in the United States, immigration officials said Wednesday. And Ustinov is losing no time in getting work here. Philip Semark, executive director of the Dallas Ballet Assn., said Ustinov signed a three-month contract to appear with the Texas company. Ustinov said through an interpreter that he and his wife had wanted to get a divorce, but that such a move was difficult in the Soviet Union. He said, however, he would try to bring his 2 1/2-year-old daughter to the United States. Ustinov said Soviet diplomatic personnel tried to persuade him to rejoin the Moscow Ballet and promised him that he would not be punished on returning home, but Ustinov said no. The Moscow Ballet--minus Ustinov--appears tonight at the Pasadena Civic Auditorium.