Born near Evergreen, Avoyelles Parish, Louisiana, Irion attended the common schools, Franklin College, Opelousas, Louisiana, and was graduated from the University of North Carolina at Chapel Hill in 1855. He studied law. He was admitted to the bar in 1857 and commenced practice in Marksville, Louisiana. He served as delegate to the State secession convention in 1860 and was opposed to secession. During the Civil War served in the Confederate States Army, being attached to General Walker's division under Colonel Randall. He served as member of the State house of representatives in 1864 and 1865. He resumed the practice of his profession. He was editor of a local newspaper in Marksville, Louisiana from 1866 to 1874. He moved to Evergreen, Louisiana, in 1870 and engaged in planting. He continued the practice of law and also engaged in literary pursuits. He served as member of the State constitutional convention in 1879. He served as judge of the third circuit court of appeals of Louisiana 1880–1884.
Irion was elected as a Democrat to the Forty-ninth Congress (March 4, 1885 – March 3, 1887). He was an unsuccessful candidate for renomination. He died in New Orleans, Louisiana, May 21, 1902. He was interred in the Baptist Cemetery, Evergreen, Louisiana.