WASHINGTON (AP) _ Supreme Court Justice William H. Rehnquist likely will not be surprised if he encounters persistent, even hostile questions this week in hearings on his nomination to be chief justice. He's been through it before.

Rehnquist was grilled for two days in November 1971 - at one point he asked permission to walk around the witness table to stretch his muscles - before being confirmed as a member of the nation's highest court.

Fifteen years later, he has been chosen by President Reagan to succeed Chief Justice Warren E. Burger and become only the 16th man to hold that job.

Sen. Edward M. Kennedy, D-Mass., was one of Rehnquist's toughest questioners in 1971. Still a member of the Senate Judiciary Commmittee, Kennedy again may challenge Rehnquist's views.

In a radio debate with Senate Majority Leader Bob Dole, R-Kan., Kennedy said Rehnquist's ''coronation may not be the smooth sailing you foresee, Bob.''

''Senators have their own responsibility under the Constitution to judge the quality of judicial nominees, especially to the Supreme Court, and it's premature for any of us to announce our conclusions now,'' Kennedy said.

Dole praised Reagan for picking Rehnquist as chief justice and Antonin Scalia, a federal appeals court judge here, for the high court.

One subject Rehnquist is sure to be quizzed about is his role in the early 1960s directing ballot security programs for Republicans in local elections in Phoenix, Ariz.

In interviews last week, three men said that Rehnquist personally challenged Democrats in a predominantly black and Hispanic precinct and intimidated some would-be voters. Rehnquist previously denied any harassment tactics.

Presidential spokesman Larry Speakes said today that questions being raised about Rehnquist are ''about the same thing that came up in the '71 hearing. We'll just leave it to Justice Rehnquist and the Senate Judiciary Committee to sort that out.''

Asked if he was confident Rehnquist would be confirmed, Speakes said, ''We're hopeful, for sure.''

In 1971, Rehnquist was the Supreme Court nominee of President Richard M. Nixon when he appeared before the Judiciary Committee.

Senate liberals challenged his views on civil rights and individual liberties. But Rehnquist often avoided giving specific answers, noting he could be called upon to decide those matters as a member of the court.

Since then, Rehnquist has compiled an extensive record as the court's most conservative justice, and there is little mystery about where he stands on major social issues.

When he testified in 1971, Rehnquist was a 47-year-old assistant attorney general and leading defender of the Nixon administration's criminal justice policies.

He pledged that as a justice he would not be guided by personal preference in deciding court cases.

''I subscribe unreservedly to (the) philosophy that when you put on the robe, you are not there to enforce your own notions as to what is desirable public policy,'' Rehnquist testified.

''You are there to construe as objectively as you possibly can the Constitution of the United States, the statutes of Congress and whatever relevant legal materials there may be in the case before you,'' he said.

When it came to specifics, he crossed swords cautiously with his interrogators.

Sen. Hiram Fong, R-Hawaii, asked him, ''Do you regard wiretapping and surveillance as very dangerous practices?''

Rehnquist replied: ''I think it would be inappropriate for me to answer that question, senator, in view of my role as advocate (for the Nixon administration). I can certainly say that promiscuous wiretapping I would regard as a very dangerous practice.''

Kennedy repeatedly asked Rehnquist to state his personal views in areas in which he previously had defended Nixon administration policies.

For example, there was this exchange:

Kennedy: ''Well, could you give us some idea which statements represent your views and which don't? We have all of us been fencing around on this.''

Rehnquist: ''I know we have. I think it would be inappropriate in an area where I have acted as an advocate to express a personal view. I realize that leaves you in an unsatisfied position.''

Sen. Birch Bayh, D-Ind., noted that Rehnquist had testfied before a congressional committee in favor of the Equal Rights Amendment for women.

''I am almost afraid to ask him whether this is the administration's view or his personal view,'' Bayh said. ''Is that a fair question that I dare?''

Rehnquist said, ''I think I must refrain from answering.''

Some senators pointed out that Rehnquist himself once suggested questioning a Supreme Court nominee about his ideology was fair game.

In 1959, Rehnquist wrote a law review article that suggested the Senate's proper role was ''thoroughly informing itself on the judicial philosophy of a Supreme Court nominee.''

When asked about his own view, Rehnquist said, ''You inevitably take yourself and your background with you to the court.'' But he said his conservatism would not hinder him in deciding each case fairly.

A few weeks later, the Senate, controlled by Democrats, voted 68-26 to confirm Rehnquist.