The Senate Judiciary Committee delayed action for one week yesterday on the nomination of Laurence H. Silberman as a federal appeals court judge to await the results of an FBI investigation into his conduct while he was a top executive of the Crocker National Bank of San Francisco.

The delay in action on Silberman's nomination to the influential U.S. Court of Appeals here infuriated committee chairman Sen. Strom Thurmond (R-S.C.), who said it was unfair because Silberman has not been accused of any wrongdoing. Thurmond angrily adjourned the committee meeting after the discussion, refusing to act on any legislation until the nomination is voted on.

Thurmond then stormed out, trying unsuccessfully to get Sen. Orrin G. Hatch (R-Utah) to walk out with him. Sen. Dennis DeConcini (D-Ariz.) protested, saying that Thurmond was trying to "alienate" committee Democrats.

Sen. Paul Simon (D-Ill.), who requested the delay, said he was not charging Silberman with any wrongdoing, but wanted Silberman's role at Crocker clarified before voting.

Crocker National Bank recently was fined $2.25 million by the Treasury Department for failure to report nearly $4 billion in cash transactions between 1980 and 1984. Most of the violations involved $3.4 billion in shipments from Hong Kong banks.

The Treasury Department said that the transactions appeared to involve large-scale laundering of drug money, a charge sharply disputed by Crocker officials.

Silberman was executive vice president of Crocker from Oct. 1, 1979, to June 1, 1983. During that time he managed the legal and government affairs departments and the corporate secretary's office.

Simon said that Democrats on the committee would like to know if Silberman knew about the matter. Simon said he has asked Silberman, and Silberman has answered that he was unaware of it.

"I have no reason to doubt it. I just want to check it out," said Simon. He said the investigation should take about a week, and would require the FBI to question about three key people. "There is a strong probability that the FBI will come in with a report saying he is clear."

Hatch, who said he has known Silberman a long time and respects him, said that there are "an awfully lot of vice presidents" at Crocker, and that it is possible Silberman was unaware of the reporting violations.

But Hatch said he felt that Simon had made "a reasonable request," as long as the FBI investigation was not used as a delaying tactic.

But Thurmond disagreed. "They can't check out something unless you've got an allegation," said Thurmond. "If you've got an allegation, come up with it."