D.C. City Council Chairman Arrington Dixon has built his constituent services fund to almost $19,000 to finance mailing newsletters, hosting receptions and dispensing political largesse to constituents. And he's spent almost half of it already.

Mayor Marion Barry, a potential political opponent of Dixon's should both men decide to seek the mayor's job next year, is trailing in the fund-raising effort, with a constituent services account this year of $16,565. And Barry also has spent about half of that sum.

And City Council member John L. Ray (D-At-Large), who is also considering running for mayor next year, has raised only $5,553 for his constituent fund since April, and has used most of that money to pay the salary of an extra person on his council staff.

The mayor and each council member are allowed to assemble funds for constituent service work -- for example, flowers for a funeral, contributions to the Boy Scouts, donations to such groups as the NAACP or for use as petty cash to pay for postage and printing costs of newsletters and leaflets. The mayor, the council chairman and each at-large council member elected city-wide are allowed to collect up to $20,000 each in a constituent services fund to pay for such expenses. Each ward council member is allowed to raise half that amount.

The mayor and all council members were required by law to file on July 1 forms detailing where that money came from and how it was spent. Barry, Dixon, Ray and Council member John A. Wilson (D-Ward 2), who raised $5,042 since April, all met the deadline. The other 10 council members have yet to file.

From the four disclosure forms made public yesterday, Dixon came out ahead, with $18,967.05 collected since the end of March, and a total of $19,098 collected in 1981.

Most of Dixon's money came from a fund-raiser he hosted last April at the posh Army-Navy Club in a penthouse overlooking Farragut Square in downtown Washington. That affair, which cost Dixon $2,853.12 for the use of the club facilities, netted the chairman $15,382.05.

Most of Dixon's contributors were bankers, most of whom gave the maximum allowable contribution of $100. Other contributors include several executives of the Potomac Electric Power Co., where Dixon's wife, Sharon Pratt Dixon, is a lawyer. On his list of $100 donors is Pepco executive vice president H. Lowell Davis, senior vice president Paul Dragoumis, executive vice president Edward F. Mitchell and vice president and general counsel Alan Kirk II.

Barry's list of contributors includes several real estate and business executives, and is heavy with city government workers and Barry administration workers and Barry administration appointees.

Out of that fund, Barry donated $150 to the Wilberforce University Alumni Association, $500 to the Crime Stoppers Club, $115 to the D.C. Youth Orchestra and $25 to the Golden Seal Club in Memphis. Barry also paid $460 to the Pigfoot Restaurant at 18th and Hamilton streets NE for refreshments provided for a meeting.