In a service that blended solemn ecclesiastical pageantry with joyful shouts of "Right on!" and "All right!," the Rt. Rev. John T. Walker was installed yesterday as the sixth bishop of the Episcopal Diocese of Washington and the first black man to hold that post.

The 52-year-old activist churchman pledged in both his sermon and his installation vows to use his position to tackle the social problems of the entire community as well asthe spiritual needs of his flock.

"I believe that the church has an important role to play in dealing with such problems as hunger, crime and aging," he said.

By church, he said. "I mean the parishes where our people live." He promised to the 93 parishes of the diocese his support "to the fullest extent possible, bringing to bear all available resources," to assist in dealing with community issues.

In yesterday's tow-hour rite at the flower and banner-bedecked Washington Cathedral, Bishop Walker received the symbol of his office, an ornate silver crozier, or bishop's cross, from his predecessor, the Rt. Rev. William F. Creighton, who Bishop Walker had served for six years as suffragan, or assistant bishop, until Bishop Creighton retired last June.

The two men embraced as the symbol of office was handed on.

Bishop Walker was formally inducted as bishop of Washington by the Rt. Rev John Maury Allin of New York, president bishop of the national 2.9 million-member Episcopal Church.

Then the soft-spoken Bishop Walker, holding his cozier in his left hand, placed his right hand on a yellowed copy of the Book of Common Prayer that had belonged to Bishop Thomas John Claggett, first Episcopal bishop of Maryland.

As his chaplain, Canon Charles Perry, held the ancient prayer book, Bishop Walker proclaimed his oath in a strong voice. He promised to "observe and to the utmost of my power, fulfull the responsibilities and customs of this office striving in all things to be a faithful shepherd."

The congregation of 2,200 confirmed his vow with a lout: "Amen! Amen."

Then escorted by Susan RIch, president of Episcopal Churchwomen of the diocese, and the Rev. William Swing, president of the diocese Standing Committee and pastor of St. Columbia's Church, the bishop walked through the congregation, acknowledging their applause. Joyous shouts of "All right!," and "right on!" greeted thge smiling bishop as he made his rounds.

Unlike the practice of the Roman Catholic Church where bishops are appointed by the Vatican, the Episcopal bishops are elected by the people. Bishop Walker was the overwhelming favorite of delegates to a special diocese convention called by Bishop Creighton 15 months ago to choose his successor.

The Georgia-born, Detroit-educated bishop came to Washington in 1966 as canon of the Washington Cathedral. He was the second black man to hold that post, the first having been the Rt. Rev. John M. Burgess, who went on to become the bishop of Massachusetts.

Bishop Burgess, now retired, was the first black bishop to head a diocese in the Episcopla Church. He was present yesterday for Bishop Walker's installation.

In his 11 years here, Bishop Walker has been involved in civic as well as ecclesiastical affairs. He has served on the District of Columbia Commission on Judicial Disabilities and Tenure and is currently chairman of the Police Chief's Citizen Advisory Council. In 1974, he headed the 15-member commission to find a police chief.

Last year he was named to the Special Commission on the United States Military Academy, appointed to examine the academy's honor system inthe wave of cheating scandals.

He has held numerous posts in the national Episcopal Church. In 1975 he represented the church at the World Council of Churches Assembly in Nairobi.

THe Washington Diocese, under Bishop Creighton was focus of a great deal of turmoil over the question of ordaining women to the priesthood. Irregular and unsuthorized ordinations of women were performed here before the larger church gave its approval to women priests and an unprecedented churhc trial took place here as the result of an irregularly ordained woman functioning as a priest.

Bishop Creighton's leadership appears to have brougth the warring elements in the diocese through the crisis and back together again. While there are still some sumblings of discontent among those who disagree with the national church's decision a year ago to ordain women, diodecan officials say no parishes here are seriously talking of schism.

Canon Perry reported that the diocese is "in very good shape," both in finances and in support for the new bishop.

In addition to the District of Columbia, the diocese includes the Maryland counties of Montgomery, Prince George's, Charles and St. Mary's.

There are 55,000 baptized Episcopalians in the diocese, but the fact that so many of them are in important positions in government and civic life gives the church influence well beyond its numbers.

Bishop Walker was born into a Methodist family in Barneville, Va. He moved with his family to Detroit when he was 2 and graduated from high school in Detroit in 1943.

He worked for the U.S. Post Office and the War Department for five years, entering Wayne State University in 1948. His involvement with an Episcopal youth group led him to join the Episcopal Church and when he finished college in 1951, he enrolled in the church's Virginia Theological Seminary in ALexandria. Three years later he became the institution's first black graduate.

He served parish churches in Michigan for three years and in 1957 became teacher of religion and history at the church-related St. Pual's School in Concord, N.H.

In the summer of 1961, he directed a church program in Latin America, where he met Rosa Maria Flores in Costa Rica. He returned six months later and married her. They have three children. He has been with the Washington Diocese since 1966.