Robert Dunkerson Orr (November 17, 1917 - March 10, 2004) was an American political leader and Governor of Indiana from 1981 to 1989. He was a member of the United States Republican Party.

Orr was born in Ann Arbor, Michigan but was raised in Evansville, Indiana. He served in the U.S. Army during World War II, rising to the rank of Major.

Robert entered state level politics when he was elected to the Indiana State Senate in 1968, representing Evansville. He served there until 1973. He was lieutenant governor of Indiana from 1973 to 1981. As governor he oversaw the reform of the state's education system. After his terms as governor, he was named as the U.S. Ambassador to Singapore, a post he held until 1992.

He died on March 10, 2004 at the Indiana University Medical Center in Indianapolis from complications following kidney surgery. He is buried in Crown Hill Cemetery in Indianapolis.