An active D.C. Democrat and labor leader filed a formal challenge yesterday to the seating of City Council Chairman Arrington Dixon as a delegate to the Democratic National Convention.

Joslyn Williams, director of the Greater Washington Central Labor Council's Committee on Political Education and a former member of the Democratic State Committee, filed the attempt to keep Dixon off the delegation with the Credentials Committee at National Democratic Party headquarters here.

Williams charged that the method by which Dixon was selected as a delegate pledged to support President Carter violated party rules. Fourteen other local Democrats, assembled by Williams, also signed the challenge -- a requirement under party procedures.

Dixon, previously chosen as a convention alternate, was named a full-fledged delegate last week by school board President R. Calvin Lockridge, who decided not to go to New York and chose Dixon to serve in his place.

But local party rules state that when a delegate chooses to give up his post and name an alternate to serve instead, as Lockridge did, the alternate "if possible" should be from the same hypothetical "congressional district" as the original delegate. For purposes of delegate selection. Washington is divided into two such districts.

Lockridge is from one district, including Wards 1, 2, 6 and 8, and Dixon is from the other, containing Wards 3, 4, 5 and 7. It would have been technically possible for Lockridge to select an alternate from his district.

The issue was raised by several supporters of Sen. Edward M. Kennedy at a meeting of the 19-member delegation last week. But delegation chairman John L. Ray ruled that since the seven-member Carter minority on the delegation was firmly behind Dixon, the appointment would stand.

The challenge will be considered by the Credentials Committee either before or during the convention, Williams said.

Dixon, vowed yesterday to "fight this thing all the way," maintaining that the rule only means a delegate who withdraws should strive to name a replacement from the same district.