Griffin was elected as a Republican to the U.S. House of Representatives from Michigan's 9th congressional district in 1956, unseating incumbent Ruth Thompson in the Republican primary. Griffin served in the House during the Eighty-fifth United States Congress as well as the four succeeding Congresses, a period spanning January 3, 1957 until May 10, 1966. After the revelations of the McClellan Committee, which investigated corruption and organized crime influence in labor unions, he and Rep. Phil Landrum sponsored the Labor Management Reporting and Disclosure Act of 1959 also known as the Landrum-Griffin Act. He later supported Gerald Ford as the Republican Conference Chairman and later, the House Minority Leader. During his tenure in the House, Griffin voted in favor of the Civil Rights Acts of 1960 and 1964, as well as the 24th Amendment to the U.S. Constitution and the Voting Rights Act of 1965, but did not vote on the Civil Rights Act of 1957. He resigned May 10, 1966 to take a seat in the United States Senate. Following the death of Sen. Patrick V. McNamara, Governor George Romney appointed him for the remainder of McNamara's term. In the 1966 election, he won election to a full term, defeating former Governor Soapy Williams by a 56% to 44% margin. He defeated Attorney General Frank J. Kelley in the 1972 election for a second term. In 1968, Griffin led a successful filibuster against the nomination of Supreme Court Associate JusticeAbe Fortas to be elevated to the position of Chief Justice, charging President Lyndon B. Johnson with cronyism, noting the close relationship between the two. Fortas resigned his Associate Justice seat in May 1969 when it was discovered Fortas had been paid a $20,000 a year retainer by Louis Wolfson, a close friend and former client, since 1966. Griffin voted in favor of the Civil Rights Act of 1968 and the confirmation of Thurgood Marshall to the U.S. Supreme Court. He became the Republican Whip Senate in 1969 and served until 1977. In 1974, he wrote to President Richard Nixon to inform him that if the White House did not release tapes that the Watergate Committee subpoenaed, the President would face impeachment and trial in the Senate. He also told the President that he considered the failure to comply with the subpoena as an impeachable offense. Up to that point, Griffin had been a supporter of the President. Griffin was an unsuccessful candidate for reelection in 1978, narrowly defeated by former Detroit City Council president Carl Levin. He initially announced in April 1977 that he would not run for re-election in 1978, saying that he was tired and that Washington needed new blood. He went on to miss a third of the votes in 1977. He changed his mind later in the campaign and Levin used his own words and his attendance record against him during the campaign. Later, Griffin served as a justice of the Michigan Supreme Court from 1987 to 1994. His son, Richard Allen Griffin, was a judge on the Michigan Court of Appeals from 1989 to 2005, when he was appointed by President George W. Bush to the United States Court of Appeals for the Sixth Circuit. During the elder Griffin's first Senate campaign in 1966, a suburban Detroit rock band, Doug Brown and the Omens, released a promotional flexidisc in support of Griffin's candidacy. The song, "Give Bob The Ball" has been included on the garage rockcompilation albumFriday At The Hideout.
Personal life
A resident of Traverse City, Griffin died on April 16, 2015, aged 91.