WASHINGTON (AP) _ The Supreme Court is asking Congress for a record $25 million budget for the next fiscal year, reflecting in part the big raises Congress gave to the chief justice and the eight associate justices.

The spending request, an 11.6 percent increase from the current budget, also includes the salary hikes Chief Justice William H. Rehnquist gave to the court's five top support officials.

Rehnquist's salary is now $160,600 a year; the court's eight other members get $153,600 annually. Just three years ago those salaries were $115,000 and $110,000, respectively.

Rehnquist's administrative assistant and the court's clerk, librarian, reporter of decisions and marshal all are paid $108,300 a year.

Among the court's approximately 325 employees, only those 14 salaries are a matter of public record. Congress no longer requires, and the court does not supply in its budgetary requests, information about individual salaries.

In the fiscal year 1992 request, $20.7 million is sought for salaries and expenses; $4.3 million for building and grounds maintenance.

Justice Sandra Day O'Connor will head a court contingent in appearances before a Senate appropriations subcommittee Feb. 28 and a House subcommittee March 14. --- Justices' Chambers Set For Computerized Face Lift

Although the court's budget request does not seek money for any major new projects, previously appropriated funds have a new priority - updating the computers used by the justices and their staffs.

In the offing is the replacement of a first generation of computers with newer PCs to be used for memo writing, opinion drafting and perhaps even the circulation of opinion drafts.

One court source who asked not to be identified said the need for updating was first recognized by recent classes of law clerks, those young lawyers who assist the justices for a year.

''These were kids who went to law school with computers far more advanced than what they found here,'' he said. --- Columbia Law Dean Wins Partial Victory on Court Fees

Until last month, the Supreme Court for years paid lawyers appointed to argue cases for death row inmates a flat $2,500 for their services. That was what the Criminal Justice Act of 1964 authorized.

But Vivian Berger, vice dean of the Columbia University School of Law, submitted a bill for over $28,000 after being appointed by the court to represent a death row inmate. She contended, and the court agreed, that a 1988 law authorized compensation in excess of the $2,500 limit.

The justices, however, unanimously approved maintaining a flat fee - of $5,000 - no matter how many hours of work are claimed by the court-appointed attorney. Berger had logged 283.5 hours of work on the case. --- Editorial Cartoon, Earl Warren Exhibits Coming to Court Building

The 500,000 tourists expected to enter the court's Capitol Hill building this year soon will have something new to see. Court Curator Gail Galloway said work would start in March on two new exhibits - one showing how the court historically has been treated in editorial cartoons and the other on the late Chief Justice Earl Warren. --- Souter Gets High Marks

Solicitor General Kenneth Starr, the Bush administration's top lawyer before the high court, was full of praise for the newest justice, David H. Souter at a recent news conference to discuss the 1990-91 term.

Asked for his impressions of Souter's performance during oral argument sessions, Starr called him ''a very artful questioner'' whose queries go ''to the heart of the case.''

''I think his demeanor ... is quite admirable,'' Starr said.