At the end of the same kind of "law and order" style speech that propelled him from the police beat to the mayor's office in 1971, Frank L. Rizzo surprised this city yesterday with an announcement that he would not seek a third term.

He said he would give up his drive to change the city charter that prohibits more than two terms for a mayor but then he hinted mysteriously that he would lead a national movement centered on the issues close to his heart. He is against public housing, special treatment for minorities, public school busing, and racial quotas. He is for the death penalty.

In the rousing speech before a nearly all-white crowd of 700, the nominal Democrat, who supported President Nixon, said, "We have to get off this kick of Democrat and Republican. That's the way they keep us divided. We have to vote the man."

The declaration taking him out of the 1979 race for mayor came at the end of his speech.

"As mayor, my hands are handcuffed," he said. "I will not seek a charter change. I will not run for mayor."

Rizzo's remarks were delivered in his native south Philadelphia, the neighborhood where the barrel-chested, 6-foot-2 lacquer-haired former police commissioner still has his strongest support.

"Four more years!" and "Governor! Governor!" were the chanted responses of the crowd to the announcement by Rizzo, who was accompanied by his cabinet and his handpicked chairman of the Democratic City Committee, Martin Weinberg.

City-wide, Rizzo's political currency has been declining in value since 1976, when he lost some support among middle-income families because he raised property taxes. Amid charges that he had been massively irresponsible in managing the city's fiscal affairs, more than 210,000 signatures were gathered on a petition to hold a recall election. However, the state Supreme Court nullified the recall section of the City Charter.

Polls, according to Democratic Party sources, show the public opposed to changing the City Charter to allow him to run again.

Also, Rizzo's health has been affected by a broken hip suffered on the scene of an oil refinery fire in 1975. He still has a steel pin in his hip and grimaces at times from the pain.

Rizzo's term will expire Jan 4, 1980. His announcement promises considerable jockeying by more than a dozen possible candidates for mayor. Among the more prominent Democrats who might seek the office:

Former U.S. Rep. William J. Green III, who lost a 1976 race for a U.S. Senate seat to Republican H. John Heinz III.

City Controller William G. Klenk, who had held on to his office for two terms despite Rizzo-backed opposition last year.

Charles Bowser, a black lawyer who lost to Rizzo in the 1975 mayoral election.

Republican possibilities include:

David W. Marston, the former U.S. attorney here who was fired by the Carter administration in January and is now running for the GOP nomination for governor in this spring's primary.

Dr. Ethel Allen, a black physician on the City Council.