Sandra D. O'Connor, a prominent Arizona jurist with Republican political credentials, has emerged as a leading candidate for the Supreme Court vacancy that will be created Friday when Justice Potter Stewart retires.

Well-placed administration officials confirmed that O'Connor, who received a high ranking from the Arizona Bar Association and was third in the Standord law school class in which Justice William H. Rehnquist finished first, had been interviewed for the job.She is believed to be the only potential nominee interviewed so far, and hers is one of a few names, most of them of women, on a "short list" reposing now with a handful of top White House aides and Attorney General William French Smith.

"She hasn't been chosen yet, but she's close," said one source.

O'Connor, a 51-year-old judge of the Arizona Court of Appeals, has enjoyed a meteoric rise through the state's political and professional circles, impressing colleagues with her intellect, demeanor, organizational abilities and conservative views. She received one of the highest ratings of any judge evaluated in a 1980 state bar poll -- 90 percent favorable.

In addition to her legal credentials, O'Connor has strong backing from Arizona's senators, Barry Goldwater (R) and Dennis DeConcini (D), a member of the Senate Judicary Committee, and from former House Republican leader John J. Rhodes.

"She's what the president's looking for," said DeConcini. "She believes in the court interpreting the law, not making it."

This was the criterion President Reagan laid down when he announced Stewart's resignation on June 18. The justice had privately made his plans known to the administration two months earlier, giving the White House and the Justice Department a head start on finding his successor.

O'Connor, an Arizona native who was raised on a cattle ranch in the southern part of the state, was appointed in 1969 to fill a vacancy in the state Senate. She subsequently won two terms and was voted majority leader, the first woman in the nation to be elected to such a leadership post. She also is the first Arizona woman to serve on the board of directors of a major bank.

Prominent Republicans including Goldwater and Rhodes urged O'Connor to run for governor four years ago, but she decided to continue her judicial career, which began in 1975 when she was elected a judge of the Maricopa County (Phoenix) Superior Court. A year and a half ago, Gov. Bruce Babbitt appointed her to the appeals court.

"There is a tendency to classify her as politically conservative," said Alan A. Matheson, dean of the Arizona State University College of Law. "She has good judgement, is articulate and well-liked." He said she has been involved in few controversial cases.

O'Connor was co-chairman of the Arizona committee campaigning for President Nixon's reelection in 1972 and was Arizona Woman of the Year that same year.

She and her husband, John, a well-known Phoenix attorney and active Republican, have three children. In the early 1960s she served as a deputy district attorney in San Mateo County, south of San Francisco, while her husband completed law school.

O'Connor is in Washington this week and was interviewed yesterday by an administration official.

Administration sources emphasized that the president has not made a decision, but one well-placed source stressed, as he did last week, that a strong effort is being made to find a "highly qualified woman." The name mentioned most, until now, is that of another conservative Republican jurist, Cornelia Kennedy of Detroit, a 58-year-old member of the 6th U.S. Court of Appeals.

One administration official said yesterday that Kennedy has support on Capitol Hill, and her name was on the list submitted to the White House by Senate Judiciary Chairman Storm Thurmond (R-S.C.).

The White House has ruled out nominating anyone in the administration for the high court vacancy, sources said yesterday. That has eliminated Elizabeth Hanford Dole, a White House aide and wife of Sen. Robert J. Dole (R-Kan.).