D.C. City Council Chairman Arrington L. Dixon and his wife, Sharon Pratt Dixon, the Democratic national committeewoman from the District, are getting divorced after 15 years of marriage, the couple confirmed yesterday.

"It's a personal and private thing. Were it not for the fact that Arrington is a public official, it would not be a matter of public discussion," Sharon Dixon, 37, said. "It's being done in a manner that is cordial and affords us mutual respect," she said.

"It's just a personal action that people go through," Arrington Dixon, 39, said. "We are in fact going through a divorce proceeding. Anything beyond that is personal."

The Dixons were married in 1966 and have two daughters, aged 11 and 13. They live on West Beach Drive in the North Portal Estates section of upper Northwest Washington.

Sharon Dixon, a lawyer who is director of consumer affairs for Pepco, has been considered a strong-willed political confidant of her husband, who is a former computer instructor at the old Washington Technical Institute and also a law school graduate.

Arrington Dixon began his political career two years after his marriage with an unsuccesful race for the Ward 5 school board seat in 1968. In 1974, he was elected to the City Council to represent Ward 4 and was reelected in 1976. In 1978, he was elected council chairman, and is expected this year to either seek reelection to that post or to run for mayor.

Sharon Dixon was elected an at-large member of the D.C. Democratic State Committee in 1976 and was first elected Democratic national committeewoman in 1977, replacing Patricia Roberts Harris who left to become secretary of Housing and Urban Development in the Carter administration. Dixon was reelected national committeewoman in 1980.

"I continue to support him politically. I have the utmost respect for him," Sharon Dixon said of her husband last night. "We had mutual differences that we couldn't resolve. We're just trying to resolve them in a way that we can still be friends."