Curtin was born on April 23, 1815, at Bellefonte in Center County. His parents were Roland Curtin, Sr. , a wealthy Irish-born iron manufacturer from County Clare, and Jane (Gregg) Curtin, the daughter of U. S. Senator Andrew Gregg. His father, with Miles Boggs, established the Eagle Ironworks at Curtin Village in 1810.
Curtin's family was prominent in Pennsylvania politics and in the Civil War. He was the great-grandson of James Potter, the vice-president of Pennsylvania, and was the grandson of Andrew Gregg, also a prominent Pennsylvania politician. He was the uncle of John I. Gregg and cousin of David McMurtrie Gregg, both Union generals in the Civil War. He also was a cousin of Col. John I. Curtin.