He was born in Lancashire, probably a younger son of John Rishton of Dunkenhalgh and Dorothy Southworth.
While a student he drew up and published a chart of ecclesiastical history, and was one of the two sent to Reims in November, 1576, to see if the college could be removed there.
With the intention of taking his doctorate in divinity he proceeded to the University of Pont-à-Mousson in Lorraine, but the plague broke out, and though he went to Sainte-Ménehould, to escape the infection, he died of it and was buried there.
At the suggestion of Robert Persons, he completed Nicholas Sanders's imperfect Origin and Growth of the Anglican Schism.
Publication of the "Tower Bills" makes it certain that Rishton did not write the diary, and his only other known works are a tract on the difference between Catholicism and Protestantism (Douai, 1575) and Profession of his faith made manifest and confirmed by twenty-one reasons.