Perk served five terms on Cleveland City Council from the city's Ward 13. In 1962, Perk was elected auditor of Cuyahoga County, the first Republican to win countywide office in a half century. He was re-elected in 1966 and again in 1970. In 1969, Perk ran for mayor of Cleveland and was defeated in the general election. In 1971, after two unsuccessful attempts, Perk won the Republican nomination for the office of mayor. He defeated future mayor, governor, and current U.S. Senator George Voinovich, then a member of the Ohio House of Representatives, in the primary election. Perk went on to win the general election and was reelected in 1973 and 1975. In 1977, however, Perk suffered an upset defeat in the non-partisan primary election for mayor.
As mayor, Perk became the subject of national ridicule on October 16, 1972, when he accidentally set his hair on fire while he attempted to use a welder's torch for a ribbon-cutting ceremony for a convention in Cleveland
Perk was again publicly humiliated after suggesting that a study on pornography ought to be conducted by municipal sanitation workers. Perk also banned the sale of Playboy Magazine at Cleveland Hopkins Airport, causing even more ridicule to fall upon him. Perk's wife, Lucille, achieved notoriety when she rejected an invitation from the First Lady Pat Nixon to an event at the White House in order to attend her regular bowling night. Later, Perk explained his wife's comment to mean that she was unable to attend because the invitation had come too late and she was unable to prepare for travel. Perk was rumored to say, "tell them it's your bowling night." Though the remark brought howls of laughter, it endeared the Perks to their ethnic base.
As mayor, Perk had a reputation of being tough with city employee labor unions. One time, the fire fighters union instigated a protest by closing City Hall one day by standing on the front steps of the building and allowing only the mail and their political allies to gain access. The ploy worked, and the fire fighters received what they were negotiating.
In 1974, Perk won the Republican nomination for the United States Senate seat formerly held by William B. Saxbe, who had resigned to accept the appointment to the office of United States Attorney General. Perk, however, was defeated soundly by Democrat John Herschel Glenn, Jr. Perk had stated that he was counting on running against the incumbent senator, Howard M. Metzenbaum, who had been recently appointed to the seat by then Governor John J. Gilligan. When Metzenbaum lost the primary to Glenn (The two were later Senate colleagues for many years.), Perk expressed doubt that he could win the election, particularly in the Democrats year of Watergate.
Perk also appointed Richard Eberling in 1973 to chair a committee to redecorate the mayor's office in City Hall, a move that proved unpopular with numerous sources. In 1974, the Cleveland Plain Dealer exposed Eberling's record as a petty criminal in a front-page story; Perk defended Eberling, and approved the financing of project until the amount significantly over-reached the budgeted amount. Eberling's lover, Obie Henderson was hired as Perk's personal secretary. Eberling was later found guilty in the death of Ethel M. Durkin, a Cleveland area widow; he also linked himself to the Marilyn Sheppard murder in Bay Village, in 1954. Circumstantial evidence also links Eberling to at least four other murders committed over a period from 1946 to 1970 that involved his stepfather, his purported girlfriend, and both of Mrs. Durkin's sisters.
Perk died in Westlake, Ohio, in 1999.
Perk's son, Ralph J. Perk, Jr., served as a municipal court judge in Cleveland from 1989 to 2003. Another son, Thomas Perk, is a council member in the village of Valley View in addition to being a fire fighter. Yet another son, Kenneth Perk, is a member of the Cuyahoga Heights Board of Education. His second youngest son, Allen G. Perk, is the President and CEO of XLNsystems Inc. in Columbus, Ohio.