Born in Natchez, Mississippi, Perkins received his early education from private tutors. He was graduated from Yale College in 1840 and from the law department of Harvard University in 1842. He subsequently was admitted to the bar in 1843 and commenced practice in New Orleans, Louisiana. He also engaged in cotton planting. He was appointed judge of the circuit court for the district comprising Tensas and Madison Parishes in 1851.
Perkins was elected as a Democrat to the Thirty-third Congress (March 4, 1853-March 3, 1855). He was not a candidate for renomination in 1854.
He served as chairman of the state secession convention in 1861. He served in the Confederate States Senate 1862–65.
Following the war, he traveled extensively in Mexico and Europe. He returned to the United States in 1878 and spent the remaining years of his life in Louisiana and Canada.
He died in Baltimore, Maryland, November 28, 1885, and was interred in Natchez Cemetery, Natchez, Mississippi.
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