Fortescue was the third and youngest son of Sir Adrian Fortescue, was educated at Winchester College. Unlike his elder brother Sir John Fortescue, chancellor of the exchequer, Sir Anthony adhered to the Roman Catholic church. During the reign of Queen Mary he married Katharine Pole, granddaughter of Margaret, countess of Salisbury, and received the appointment of comptroller of the household of his wife's uncle, Cardinal Pole. After the accession of Elizabeth, Sir Anthony and his brothers-in-law Arthur and Edward Pole plotted against the new sovereign.
In November 1558 Fortescue was taken into custody along with several persons whom he was accused of causing to cast the horoscope of Elizabeth and to calculate the length of her life and the chances of the duration of her government; he was, however, released on bail on 25 November, and no further action seems to have been taken in the matter (Strype, Annals, ed. 1825, vol. i. pt. i. pp. 9–10). Three years later, in October 1561, Arthur and Edward Pole and Fortescue were arrested as they were on the point of sailing to Flanders; they were kept in prison until February of the next year, when they were tried upon a charge of high treason at Westminster Hall. There is no complete record of the trial extant; from the accounts given in Strype's ‘Annals’ (vol. i. pt. i. pp. 555–6), and Wright's ‘Queen Elizabeth’ (i. 121, 127, 129), their plan seems to have been wild. They proposed as soon as they arrived in Flanders to proclaim Arthur Pole, the elder of the brothers, Duke of Clarence; to persuade Mary Queen of Scots to marry Edmund Pole the younger brother, Arthur being already married to a daughter of the Earl of Northumberland; to obtain from the Duc de Guise a force of five or six thousand men, with whom they hoped to return to Wales, proclaim Queen Mary, overthrow the existing government, and restore the ancient religion.
Before setting out on this expedition they had consulted two conjurers, by name John Prestall and Edward Cosyn, who, with two servants of Lord Hastings and a person named Barwick, were arrested and included in the indictment. These conjurers had succeeded in raising a ‘wicked spryte’ who prophesied that all would go well with their designs, and that Queen Elizabeth would die a natural death before the next summer. A more serious clause of the accusation charged Fortescue with obtaining countenance and help from the French and Spanish ambassadors. All the accused were convicted and condemned to death, but their lives were spared by the queen, and their sentences commuted to imprisonment in the Tower. There, between 1565 and 1578, both the Poles died, while Fortescue, at what date is unknown, was released or allowed to escape. He probably owed his freedom to the influence of his brother Sir John, who was highly esteemed by Elizabeth. Of the remainder of his career nothing is known; he is spoken of as living, probably abroad, in his brother Thomas Fortescue's will, dated May 1608.
Sir Anthony left three sons, Anthony, John, and George; his grandson Anthony, son of his eldest son, was appointed by Charles III, Duke of Lorraine, his resident at the English court, and was expelled from the country by a resolution of the House of Commons, 16 Oct. 1644.