Rainsford was the second son of Robert Raynsford of Staverton, Northamptonshire and his first wife Mary Kirton, daughter of Thomas Kirton of Thorpe Mandeville Northamptonshire. He matriculated at Exeter College, Oxford on 13 December 1622, but left the university without a degree. He was knighted by 1622. In 1630 he was elected recorder of Daventry, being then a student of Lincoln's Inn, where he was called to the bar on 16 October 1632. In 1653 he was chosen recorder of Northampton.