The Rev. Billy Graham announced yesterday that he will conduct an evangelistic crusade at the Washington Convention Center next April 13 through 20, his first in the nation's capital since 1960.

Graham, a spiritual and sometimes political adviser to presidents since Eisenhower, pledged he would try to "stay completely out of partisan politics, whether local, national or international," and would simply "preach the gospel of Jesus Christ."

But that gospel, he said, "touches on many things which may have political dimensions, although they are not partisan, because beneath these social issues are moral and spiritual issues."

The Graham organization is not unfamiliar with the problems those "political dimensions" can create. Twelve years ago, an effort to organize a crusade here failed when both the D.C. Council of Churches and the black Baptist Ministers Conference withheld their backing.

Reflecting anti-Vietnam war sentiment of the time, the Council of Churches faulted Graham, who preached frequently at the Nixon White House, for his failure to publicly repudiate the "indiscriminate bombing of persons and of property in Vietnam."

The black Baptist preachers charged Graham with "insensitivity" on racial issues. The Graham organization had bypassed most inner-city black pastors, drawing instead on sympathetic southern congressmen and suburban pastors in attempting to put together a local sponsor.

This time, the Council of Churches is an integral part of the Washington crusade committee. Colleen Townsend Evans, speaker and author of religious books who heads the local committee, is believed to be the first chairwoman of a Graham crusade committee. Former mayor Walter Washington is honorary chairman.

Graham crusades are always rooted in local churches, which provide volunteers, enthusiasm and planning and also share in the new converts the evangelistic missions are designed to generate.

Graham, who has distanced himself from successive occupants of the White House since the Nixon years, said at a news conference yesterday that he had not discussed the upcoming crusade with President Reagan.

Graham said that in addition to evening mass meetings at the convention center, he and "international and interracial" teams of evangelists will conduct "scores and perhaps hundreds of other meetings both in the inner city and in the suburbs" around the main crusade events.

"The number one problem in our world is alienation," the evangelist said, "rich versus poor, black versus white, labor versus management, conservative versus liberal, east versus west . . . . But Christ came to bring about reconciliation and peace."

Asked to apply the reconciliation concept to the current controversy over Reagan's scheduled visit to a German cemetery where some Nazi storm troopers are buried, Graham steered clear of partisan politics, responding: "It's good to have reconciliation all over the world."

But for "those who went through the Holocaust," he added, "it may be too early and the wounds too deep" to expect reconciliation "in their lifetime."

Graham is scheduled to address area clergy at Shiloh Baptist Church at 10 a.m. today.