Johnathan Rodgers, for the past five months executive producer of the low-rated "CBS Morning News," was named yesterday to be vice president and general manager of WBBM-TV, the CBS-owned station in Chicago that has been experiencing not only ratings troubles of its own, but serious relations problems with Chicago's black community.

No replacement for Rodgers at the "Morning News" has been named.

Representatives of the Rev. Jesse Jackson's Operation PUSH have picketed the Chicago station since November over the demotion of a popular black anchor, Harry Porterfield, who has since taken a job with the ABC-owned Chicago station, WLS-TV. On Tuesday, Jackson met in New York with CBS News President Van Gordon Sauter, CBS-owned stations chief Neil Derrough and other CBS executives.

Then, yesterday morning, Rodgers, who is black, was asked to take the WBBM job. CBS spokesmen said Rodgers was chosen on the basis of his professional qualifications, not his race. The Rodgers appointment "was not discussed at our meeting with Rev. Jackson," CBS corporate spokesman George Schweitzer said. "We do not make decisions that way."

Frank Watkins, a spokesman for Jackson here, concurred that "this is no case of, quote, getting a black to fill the position. Johnathan Rodgers is an eminently qualified person."

Rodgers, 40, joined CBS News in 1983 after serving first as news director, then as station manager, at KNXT (now KCBS), the CBS-owned station in Los Angeles. During a career considered dazzling by industry insiders, Rodgers has also been executive producer of the weekend "CBS Evening News," and, in 1976, assistant news director at WBBM. He was named executive producer of the "Morning News" last November.

At about that time, Bill Kurtis, who had been "Morning News" anchor, was returning to Chicago and an anchor position at WBBM, in a flurry of fanfare. But news ratings for the station did not go up with Kurtis' return, and the demotion of Porterfield proved an unpopular move. WBBM general manager Gary Cummings, the man Rodgers is replacing, resigned two weeks ago.

The PUSH picketing of WBBM, and calls for a viewer "boycott" of the station, were in protest of hiring practices at the station. The picketing was reportedly to be carried to CBS-owned stations in other cities. An Operation PUSH spokesman in Chicago could not confirm yesterday whether other stations had been picketed, but the receptionist at PUSH headquarters answered the phone, "Boycott CBS; Operation PUSH."

The CBS-owned stations division issued a statement that said, "With respect to any PUSH boycott at our other stations, we feel such actions would be premature. There have been no discussions between PUSH and our other stations yet. We have told PUSH that we are willing to meet with them and discuss their concerns at the other stations."

CBS executives praised Rodgers yesterday for his expertise in both news and management. CBS News Executive Vice President Howard Stringer said, "My attitude is one of enormous admiration for Johnathan. We'll miss him sorely, but this is a great opportunity for him. Now we have to move quickly and firmly, reshaping the 'Morning News' to make it competitive in the spring."

Stringer said Rodgers had given the program "life and energy." He would not speculate on Rodgers' replacement, though insiders said David Corvo, the program's executive editor, was on the inside track.

In a statement, Derrough said Rodgers was "uniquely qualified for the job" and that he had "complete confidence in his ability to manage WBBM-TV." Schweitzer said, "Clearly, if you look at his credentials, Johnathan Rodgers had been groomed to be general manager of a CBS television station. There is no doubt about it."