Exxon Corp., the world's largest petroleum company, has sold its retail heating oil delivery service in metropolitan Washington to another oil giant - Atlantic Richfield Co.

Griffith-Consumers Co., since 1957 a wholly owned Arco subsidiary, paid about $1 million in cash for the local Exxon routes, equipment, burner and office equipment and oil trucks on June 1.

Already the largest oil heat equipment and supply company in the Washington-Baltimore region, Griffith-Consumers serves more than 30,000 customers.

If the former Exxon customers switch to Griffith, the company could pick up an additional 8,300 retail consumers in the metropolitan area. Exxon provided home and office heating oil throughout the District, Montgomery and Prince George's counties in Maryland, and Alexandria and Fairfax, Arlington and Prince William counties in Virginia.

A letter to former Exxon customers, from Griffith President Pierce MacNair, said the Cheverly-based company "will assume the responsibilities of your heating oil agreement and your burner service contract with Exxon."

However, consumers are free to make contracts with other oil delivery firms.

Exxon retail oil heat manager R. T. Rozanski, in Baltimore, said Exxon as tranferred budget and remaining regular account balances to Griffith, which has annual sales in excess of $26 million.

Exxon, which has been engaged in the oil heating business here for at least 32 year, began a program of selling its retail oil heat businesses around the country in 1968.

Mary Tobin, an Exxon spokeswoman in Baltimore, said yesterday the company concluded that smaller distributors could "do a more efficient job . . . it was profitable but when we compared our businesses [Exxon] found the smaller firms had lower operating costs . . . we figured the situation wouldn't improve."

Several years ago, Amoco Oil Co. sold its retail heating oil business to another local company, A. P. Woodson.

As Exxon has withdrawn from the business, Griffith-Consumers has been expanding.

Starting in 1898 by Ward W. Griffith as a sole proprietor delivering coal and ice with horse drawn wagons, Griffith merged with Consumers Co. in 192. Since the 1950s, Griffith has acquired John P. Agnew Co., the domestic business of L. P. Steuart & Bros., Brookland Co., Globe Oil and O'Malley-Sexton Co.

Griffith-Consumers recently moved to a new $1 million corporate headquarters at the Cheverly industrial park. Regional offices are located at the Alexandria industrial park and in Elkridge, a Baltimore suburb.

Exxon will continue to operate from a terminal in Fairfax, supplying wholesale customers with gasoline, oil and diesel fuel in the metropolitan area, Tobin said.