Born Alexander Thompson MacKaye in Scotland. Apprenticed to a bookbinding tools manufacturer. Went to London in 1850 and worked for punch-cutting expert John Skirving, where he cut typefaces for prominent English typefounders, such as Henry Caslon, Vincent Figgins, and the Stephenson Blake company. Took the offer of a full time position at the L. Johnson & Co. in Philadelphia in 1854, where he changed his surname from MacKaye to Kay. He stayed with L. Johnson & Co (later Binny & Ronaldson, then MacKellar, Smith & Jordan) for 40 years, until he lost much of his sight to cataract. He also spent several years engraving dies for minting coins at the Philadelphia mint.

Of the many Roman faces Alexander Kay designed and cut in Philadelphia, his most famous are Binny Old Style and Ronaldson Old Style.