The U.S. Customs Service has come up with an unorthodox way to cut its printing budget that its originator says could "revolutionize" the way the federal government does business.

The idea is to get entrepreneurs to begin reproducing government forms for a profit, a notion that has raised some eyebrows since it came off the drawing boards.

Stephen A. Jacobs, a special assistant to the commissioner of the Customs Service, came up with the idea this summer after he boarded a plane and was handed a packet jammed with discount coupons, travel tips and advertising.

The packet, Jacobs decided, was just what Customs needed for "Operation First Impression," the agency's campaign to make a tourist's arrival in this country easier and more pleasant.

What better way to greet travelers, Jacobs mused, than with an informational packet that contained greetings from President Reagan and Customs Commissioner William C. von Raab, a declaration form and instructions for filling it out, and tidbits about what may and may not be brought into the country?

Jacobs called Richard M. Shalowitz, president of Custom Advertising of Elk Grove Village, Ill., which had printed the airline packet, and asked him how much it would cost to print 30 million declaration packets for Customs. Shalowitz estimated that it would take $1.2 million to produce and print a slick 4 1/4-by-8 1/2-inch booklet with a full-color photograph of Miss Liberty on its cover.

But other Customs officials balked. In fiscal 1982 the agency had budgeted only $300,000 for printing the declaration forms.

That's when Jacobs and Shalowitz started talking about advertising, six full pages of it in each packet. Shalowitz said he could charge $50,000 per page for a month, which would generate about $3.6 million. That would be enough to give Customs a 15 percent cut and make a profit for his company, he said.

Everyone at Customs liked the idea, Jacobs said, except the agency's legal staff. It warned von Raab that it is illegal for a federal agency to sell advertising in a government document unless Congress has granted a special waiver.

The project seemed doomed until Jacobs and Shalowitz had another brainstorm. They asked if Shalowitz could copy the official declaration form and include it in his packet. Customs decided he could and it agreed to accept his forms at entry points. Officially, Customs has no connection with Shalowitz' project and will not receive any profits from it, agency spokesman Dennis Murphy said yesterday. But Customs will make Shalowitz' packets available -- along with its own -- when airlines and ship companies pick up the forms for their passengers, Murphy said.

Customs believes that Shalowitz' packet will be so popular that the government eventually will be able to reduce the number of forms it prints, and thus its printing costs, Murphy said.

The Government Printing Office has approved the plan. "Damn few government documents are copyrighted," said Garrett Brown, the GPO's general counsel, "so I don't see how they Customs can start or stop someone" from reproducing the forms. Customs' chief counsel, Richard Abbey, won't reveal what advice he gave von Raab, saying his advice is protected by the lawyer-client privilege. An agency source, however, said Abbey's office has raised a number of questions about the legality of the plan.

Murphy said the agency did not try to find out if other firms would be interested because it was primarily Shalowitz' idea, not theirs. He added that other firms would be allowed to copy the forms if they wished. Shalowitz said he has a patent pending on the brochure Jacobs saw on the plane, and is investigating whether the brochure with the declaration form could be patented. Shalowitz said he plans to produce the first packets in February and has sold advertising to Diners Club, National Car Rental and Philip Morris Co.