Interior Secretary Cecil D. Andrus, in an unusual announcement, yesterday ordered Standard Oil Co. of California to step up its oil exploration in the Santa Barbara Channel, or be forced to give up its interest in eight federally leased tracts.

"My policy is that exploration and development activities must proceed in a prompt and efficient manner," Andrus wrote in a letter to Chevron U.S.A., Inc., Standard's operating company.

Under a 1953 law, the Outer Continental Shelf Act, Interior is required to oversee the expeditious development of offshore tracts it leases to the oil companies.

Chevron declined comment on yesterdays' action.

Andrus, however, was the first Interior secretary to assign a high priority to expediting oil and gas development on lands leased by Interior's Bureau of Land Management. He has also called on Exxon, Union Oil Co., and Texaco to step up exploration efforts off the California coast.

"To the best of my knowledge this has never been done before," said David Page, an Interior official on the Lease Review Committee Andrus set up two years ago.

Chevron told Interior last year that it planned to drill an exploratory well last month, and begin a second exploratory well by Jan. 15. The company, however, missed its deadline because the scheduled drillship was drilling a well in San Pedro Bay, which is also off the California coast. Chevron had earlier asked Andrus for a delay til Jan. 28, or latter if it found oil or gas in San Pedro Bay.

The Interior Department, however, says that Chevron should not have begun drilling in San Pedro Bay if it resulted in falling behind in its scheduled exploration in the Santa Barbara Channel.

The tracts involved were leased by Interior in 1968, are known as the Santa Clara unit and are located nine miles west of Oxnard, Calif. They are owned jointly by Atlantic Richfield Co., Exxon, and Union Oil Co. Chevron, under an agreement signed with the Interior Department in 1973, is the drilling operator on the eight leased tracts in question.