The term “psychometry” was coined by American scientist J. Rhodes Buchanan in 1842. (From the Greek psyche = spirit/mind and metron = measure, hence “soul-measuring”.)
As a mentalism plot, it was popularized by Theo Annemann in the June 1935 Jinx, No. 9, p. 36. However, there is a record of exactly that presentation used by an English medium, J. Burns, as early as 1885.
Also note “Der Hellseher” in F. W. Conradi's Der Moderne Kartenküstler, 1896, p. 80; repeated in A. Roterberg's New Era Card Tricks, 1897, p. 144, as “X-Rays”. These are the first published descriptions of a method. The marks were on the outside of the envelopes. Annemann's placement of them inside was more subtle.