Carr engaged in the tobacco business at an early age and continued in it until the outbreak of the Civil War. He was then a colonel of militia, having entered that service in 1849 and risen rapidly. On May 14, 1861, he was mustered into the service of the United States as colonel of the 2nd New York Infantry and sent to Ft. Monroe, Va. Of the experiences of the green troops there, and of the action at Big Bethel (June 10), --dignified at the time by the name of battle, --he later wrote in Battles and Leaders of the Civil War, II, 144-52. He soon succeeded by seniority to the command of the brigade, which belonged to the 2nd Division of the 3rd Corps, and led it in the Peninsular campaign and at the second battle of Bull Run. On September 7, 1862, he was appointed brigadier-general of volunteers, by a recess commission under which he served until March 4, 1863, when the adjournment of the Senate without confirmation of his nomination terminated the appointment. He was promptly reappointed, however, March 30, 1863, and in due time this nomination was confirmed. He continued to command a brigade, except for a short time when the death of Gen. Barry, killed at Chancellorsville, put him in charge of the division. The 3rd Corps (Sickles) was the one which occupied the salient in the center of the Union line and bore the brunt of the Confederate attack on the second day of the battle of Gettysburg. The division commander (Humphreys), in his report of the battle, refers to Carr's "cool courage, determination and skillful handling of troops. " On October 4, 1863, Carr was assigned to the command of the 3rd Division, 4th Corps. In the following spring he joined Butler's Army of the James, which was to move against Richmond from the southeast while the Army of the Potomac advanced from the north. He commanded a division of colored troops in the operations around Petersburg, and for some time was in charge of the defenses on the York and James rivers. After being mustered out of service, August 24, 1865, he took up manufacturing in Troy. In 1867 he was appointed major-general of militia, and held that position for the rest of his life. For many years he was active in political life, being elected secretary of state in New York in 1879, 1881, and 1883. He was the Republican candidate for lieutenant-governor in 1885, but failed of election. He died in Troy.
He served as Secretary of State of New York from 1880 to 1885, elected in 1879, 1881, and 1883. In 1885, he ran on the Republican ticket for Lieutenant Governor of New York with Ira Davenport, but was defeated by Democrat Edward F. Jones.