Scrope matriculated at Hart Hall, Oxford, on 7 November 1617, and became a student of the Middle Temple in 1619. In November 1624 he married Mary, daughter of Robert Waller of Beaconsfield, a sister of the poet Waller.
At the opening of the civil war he raised a troop of horse for the parliament, and in 1646 was major in the regiment of horse commanded by Colonel Richard Graves. When the army and parliament quarrelled, Scrope took part with the soldiers, and possibly helped Joyce to carry off Charles I from Holdenby to Newmarket. He succeeded to the command of the regiment about July 1647.
In June 1648, at the outbreak of the Second English Civil War, Scrope was ordered to join Colonel Whalley in the pursuit of the Earl of Norwich and the Kentish royalists, and he took part in the siege of Colchester. At the beginning of July he was detached from Colchester to pursue the Earl of Holland, whom he defeated and took prisoner at St. Neots on 10 July. He was then sent to suppress some disturbances at Yarmouth; caused by the threatened landing of the Prince of Wales.
Scrope took part in the deliberations of the council of the army which resulted in the rupture of the treaty of Newport; was appointed one of the king's judges, and attended the meetings of the court with exemplary regularity. His name appears twenty-seventh among fifty-nine judges who signed the death warrant.
Scrope's regiment was one of those selected by lot for the expedition for the reconquest of Ireland (20 April 1649); but early in May 1649 they mutinied, refused to go to Ireland, and demanded the re-establishment of the representative council of agitators which had existed in 1647. On 15 May Cromwell and Fairfax surprised the mutineers at Burford, and the ringleaders were tried by court-martial and shot.