President Reagan nominated District of Columbia Corporation Counsel Judith W. Rogers yesterday to a seat on the D.C. Court of Appeals, the city's highest court.

The nomination, expected to be approved by the Senate, prompted widespread speculation both on Rogers' successor as the city's chief legal officer and on her possible impact on the court, which has been sharply divided under current Court of Appeals Chief Judge Theodore R. Newman Jr.

Rogers, 43, a former assistant U.S. attorney here, has been corporation counsel since her appointment by Mayor Marion Barry in 1979. She would serve a 15-year term on the nine-member appeals panel, filling a seat vacated three months ago by Judge Catherine B. Kelly, a longtime liberal ally of Newman's on the court.

Newman has reportedly decided not to seek reappointment next year as chief judge of the court, and has been actively seeking a job in the private sector. See Page A20.

Reagan also nominated Bruce D. Beaudin, 43, director of the D.C. Pre-Trial Services Agency and a former director of the D.C. Public Defender Service, and A. Franklin Burgess Jr., 40, chief of the appellate division at the D.C. Public Defender Service, to fill two vacancies on the D.C. Superior Court.

Those vacancies were created by the retirements in March of Judges John D. Fauntleroy and Joseph M.F. Ryan.

Lawyers both inside and outside the Barry administration said yesterday they believed Rogers could prove a valuable addition to a court split for years by differences of personality and ideology.

One lawyer who knows Rogers well said she was "too smart to fall into" any one camp on the court. That lawyer and others, all of whom asked not to be named, said that Rogers' years as a federal prosecutor from 1965 to 1968 would make her inclined to be a "hardliner" on criminal matters, but added that she would probably be a strong backer of the city on home rule issues.

Newman called Rogers an "outstanding choice" and said he "looked forward with pleasure to her imminent confirmation."

Rogers said in an interview yesterday that she was "honored when the nomination commission sent my name to the president and I'm honored that the president has nominated me." She said she was "very excited" about the possibility of serving on the District's highest court, which she called a "demanding job."

But Rogers declined to comment on her specific legal views, saying it was not the "appropriate time" to do so.

"We've been expecting the nomination ; I think she'll be good," said one top Barry aide.

The official described Rogers as a good lawyer but not a skilled administrator, and said she has had problems in keeping the corporation counsel's office functioning smoothly, instead jumping from crisis to crisis. Rogers has complained of staff shortages in the office.

The Barry administration official expressed doubts that the mayor would choose one of Rogers' assistants to succeed her, except perhaps as acting head of the office until a permanent replacement is found.

David A. Splitt, the city's former director of documents, a cabinet-level post, normally would be considered a candidate, that official said, adding that Splitt was respected by Barry and did a good job of cleaning up the city's legal records and in troubleshooting the many problems at the D.C. elections board.

However, the official said, Splitt--who left the government for private law practice after he was not offered a better job in the administration, and who reportedly courted the corporation counsel's job after it became known that Rogers might leave--could face opposition from some Barry aides because of his jealously guarded independence.

Another possible successor to Rogers is Pauline Schneider, director of intergovernmental relations, a post Rogers held under former mayor Walter E. Washington. However, the official was unsure whether Schneider has had enough legal experience for the job.

Several lawyers said that if Barry looks outside the administration to fill Rogers' job, one choice could be Howard University Law School Dean Wiley Branton, who is close to Barry.

But Branton said yesterday that "Nobody's asked me, and I wouldn't take the job."