WASHINGTON (AP) _ The celebration of the Constitution's 200th birthday begins Sept. 16 in Washington with President Reagan leading the nation in a reading of the Pledge of Allegiance, former Chief Justice Warren Burger announced today.

The next day, the scene of the festivities will shift to Philadelphia, where the Constitutional Convention completed its work 200 years ago, Burger said.

Burger, chairman of the Commission on the Bicentennial of the U.S. Constitution, joined several corporate sponsors of the celebration at a news conference today in announcing plans for what they called ''A Celebration of Citizenship.''

The Sept. 16 activities are scheduled to begin at 1:30 p.m. EDT, with Reagan's reading of the pledge from the steps of the Capitol. He will be joined by Burger, who will read the Preamble to the Constitution; Senate Majority Leader Robert Byrd, D-W. Va.; House Speaker Jim Wright, D-Texas; and a crowd of children estimated to be in the thousands.

In answer to questions today, Burger said he did not believe that the visit of Pope John Paul II that week, nor the start of Senate Judiciary Committee hearings on the nomination of Robert Bork to the Supreme Court, will take attention away from the Constitution's celebration.