Pope John Paul II appointed the Most Rev. Alvaro Corrado del Rio as an auxiliary bishop of the Washington archdiocese yesterday, the first Puerto Rican to be named a bishop of the church in this country and the first Hispanic bishop here.

Corrado "will serve all the people in the archdiocese," Archbishop James A. Hickey said yesterday at a press conference called to introduce the prelate, who is a Jesuit. But, Hickey said, "I will rely upon him to help me in ministering to the Hispanic people."

Church leaders estimate that within the Washington archdiocese, which includes the District of Columbia and five southern Maryland counties, about 20 percent of the 380,000 Catholics are Hispanic and 20 percent are black.

Hickey said that just as Auxiliary Bishop Eugene Marino "has all the care for black Catholics, I will ask Bishop Corrado to do the same for Hispanics." He said that for administrative purposes, he will divide the archdiocese into three geographical units with Corrado, Marino and Auxiliary Bishop Thomas W. Lyons each in charge of a segment.

As head of the church in the nation's capital, Hickey has been playing an increasingly prominent role in the National Conference of Catholic Bishops. He indicated this was a factor in requesting another auxiliary.

With three auxiliary bishops here, "It will ease my conscience that I am not neglecting my own people," he said.

At 43, Corrado has had a colorful career but one largely devoid of the conventional steppingstones to a bishop's appointment. His ministry since ordination in 1974 has been divided between Puerto Rico and New York in roles as varied as lecturing at the Metropolitan Museum of New York, counseling Spanish-speaking prisoners at New York's Riker's Island Prison, and directing a retreat center for married couples in Aibonita, Puerto Rico.

His sole parish assignment was a three-year stint as assistant pastor at Nativity Church in New York's Bowery. Since 1982, he has been with the Northeast Catholic Hispanic Center in New York, coordinating the church's work with Hispanics in 36 dioceses.

Born in Puerto Rico, he entered the seminary there to begin studying for the priesthood at the age of 12, and at 18 traveled to Poughkeepsie, N.Y., to enter the rigorous Jesuit novitiate. He has studied at Fordham University, the now-extinct Woodstock College and at the Institut Catholic in Paris.

He spent a year working with the poor in the slums of Medellin, Colombia, as part of his Jesuit training. Corrado, who becomes the 17th Hispanic bishop of the church in this country, is the only Jesuit bishop within the contiguous 48 states.

The new bishop is the seventh of 14 children. A brother, Baltasar, served eight years in Congress as the resident commissioner from Puerto Rico and is currently mayor of San Juan. Three of his sisters and three of his mother's sisters are nuns.

He said yesterday that when he called his mother in Puerto Rico to tell her he was to become a bishop, she burst into tears and exclaimed, "That means you're not going to come back to Puerto Rico!" But she promised to be on hand, he said, for his installation on Aug. 4 at the Shrine of the Immaculate Conception.