Atlantic Richfield Co. yesterday became the first major oil company to drop its credit card operations entirely, announcing that after April 14 the company will accept only cash.

The company, which has 2.9 million credit card accounts, said it will notify its customers by letter that it is discontinuing its credit card operations. In addition to getting rid of its own credit card, Arco also will refuse all other credit cards.

Credit handling in 1981 cost the company approximately $73 million, company spokesman Tony Hatch said. He also said 70 percent of the company's customers use cash rather than credit cards already.

"We realize this is a bold step," said James Morrison, president of Arco Petroleum Products Co. "We considered various alternatives and concluded that our dealers and customers would benefit most by doing away entirely with the credit card system." Beginning April 1, signs on top of gasoline pumps at Arco stations will announce the end of credit at those outlets.

The savings from eliminating credit operations will be passed on to dealers and distributors in the form of a 3-cent-a-gallon reduction in the price of gasoline.

Whether that savings gets passed on to Arco's customers is up to the dealers, who are independent, Hatch said. But he added that the company has recommended they do so and that similar recommendations generally have been accepted.

Although no other major oil companies have decided to drop their credit card operations, other oil companies are looking at options. Exxon has a pilot program in Phoenix in which it offers customers who pay cash a discount, and Texaco requires its service station dealers to pay a processing fee on all credit card invoices they submit to the company. Amoco also is test-marketing a gasoline discount-for-cash program in several markets.

"We believe there are other companies--not just in the petroleum area--that are going to look very closely at this," Hatch said.

The Nilson Report on credit cards predicted in December that all major petroleum marketers would begin charging consumers for use of credit in one way or another.

Since the imposition of credit controls in 1980, retailers, oil companies, bank card companies and others have been experimenting with a variety of options to help recover the cost of extending credit. A West Coast regional gasoline marketing firm, USA Petroleum, is testing a debit card system in which gasoline charges would be deducted automatically from a customer's savings and loan account.