President Reagan marked George Washington's birthday yesterday by attending services in 209-year-old Christ Church in Alexandria which the first president helped organize.

It was the third time since his inauguration more than 13 months ago that he attended church. Reagan's two other church outings here were at the National Presbyterian Church in Northwest Washington.

He and Mrs. Reagan attended the venerable Alexandria church in response to an invitation from the rector, the Rev. Dr. Mark S. Anschutz, and to the tradition that the president should attend the church some time during his incumbency. "We've had all the presidents in recent years except Nixon and Kennedy," said Anschutz.

The president and Mrs. Reagan sat in Washington's pew and joined in a "Prayer for America," which Washington wrote. It read, in part: "Almighty God, we make our earnest prayer that Thou wilt keep the United States in Thy holy protection; that Thou wilt incline the hearts of the citizens to cultivate a spirit of subordination and obedience to government; to entertain a brotherly affection and love for one another and for their fellow citizens at large."

It was the first of several events during which Reagan will honor Washington. He will lay a wreath and speak briefly today at Washington's tomb and tour Washington's residence.

Members of Christ Church and visitors queued up outside the iron fence around the church's burying ground on North Washington Street more than an hour before the 11:15 morning prayer service. At the door of the weathered brick church, everyone passed through a security check and a metal detector similar to those at airports.

White House aides attribute Reagan's infrequent attendance to the rigid security measure imposed at any of his appearances since the reports of alleged Libyan assassination attempts. The Secret Service now requires that for any appearance before a mass gathering, all members of the crowd must be screened.

Last fall, when they learned of this new regulation, National Presbyterian volunteered to permit electronic screening devices in the entrance to the sanctuary for any service the president wanted to attend.

Nearly every president has gone to church regularly while in the White House.

Dwight D. Eisenhower had no church ties but was baptized and became a member of National Presbyterian Church after he became president, and attended fairly regularly. Harry S Truman, a lifelong Baptist, faithfully attended First Baptist Church, which later became Carter's church.

Reagan continues to appear before conservative religious group--earlier this month he addressed both the national prayer breakfast and the National Religious Broadcasters' convention. He credits God with having saved his life during the assassination attempt last March 30.