Born in Bellefontaine, Ohio, Kennedy attended the public schools and Geneva College in Northwood, Ohio. He was commissioned as a second lieutenant in the 23rd Ohio Infantry in June 11, 1861. He served as a captain and assistant adjutant general dating from October 7, 1862, and was promoted to major and assistant adjutant general on November 16, 1864. He resigned April 8, 1865.
Kennedy was commissioned as colonel of the 196th Regiment, Ohio Volunteer Infantry, on April 14, 1865. He was brevetted as lieutenant colonel of Volunteers and brigadier general of volunteers, both dating from March 13, 1865.
Upon the end of the war and his resignation from the volunteer army, Kennedy returned to Bellefontaine, where he studied law. He was admitted to the bar in 1866 and commenced practice in Bellefontaine. He was appointed by President Rutherford B. Hayes as collector of internal revenue for the fourth district of Ohio, serving from 1878 to 1883. He was the Lieutenant Governor of Ohio from 1885–87.
Kennedy was elected from Ohio's 8th District as a Republican to the Fiftieth and Fifty-first Congresses (March 4, 1887 – March 3, 1891). He was not a candidate for renomination in 1890.
He was appointed by President William McKinley in 1899 as a member of the Insular Commission, which was directed to investigate and report upon conditions existing in Cuba and Puerto Rico and served as its president.
Robert P. Kennedy died in Columbus, Ohio, and was interred in the Bellefontaine Cemetery.
Despite his name and profession, he was not related to the Kennedy political family.
- Lawrence Kestenbaum. "The Political Graveyard". http://politicalgraveyard.com/bio/kennedy7.html. Retrieved 2008-11-15.
- Robert P. Kennedy at the Biographical Directory of the United States Congress Retrieved on 2008-10-18
- Lawrence Kestenbaum. "The Political Graveyard". http://politicalgraveyard.com/families/1427.html. Retrieved 2008-11-16.
- Robert P. Kennedy at Find a Grave Retrieved on 2008-10-18
! colspan="3" style="background: #cccccc" | United States House of Representatives
|- style="text-align: center;"
|width="30%" align="center" rowspan="1"|Preceded by
John Little |width="40%" style="text-align: center;" rowspan="1"|U.S. Representative from Ohio's 8th Congressional District
1887-1891 |width="30%" align="center" rowspan="1"| Succeeded by
Darius D. Hare |- |}
Template:Governors of Ohio