Max Maven believes the earliest published instance of this method of confirming the identity of a torn and restored card is in Henri Decremps's La magie blanche dévoilée, 1784, p. 12 of the English translation. Decremps claims to expose the methods (and hence the effects) of Giovanni Giuseppe Pinetti, based on a performance observed in 1783. The routine references above is “The Card Nailed to the Wall by a Pistol Shot,” which used a version of the torn-corner identification.
That routine, along with the torn corner idea, was republished several times across many books throughout the nineteenth century. The concept began branching out in other tricks near the end of the century, with a torn and restored card in Professor Hoffman's Modern Magic, 1876, p. 98; August Roterberg's New Era Card Tricks, 1876, p. 75; William John Hilliar's Modern Magicians Hand Book, 1902, p. 59; and a rising card in Hoffmann's Drawing Room Conjuring, 1887, p. 42. Published versions continued to appear with increasing frequency, during the early 1900s. By the 1920s, the idea had become standard, with dozens of applications.