1650s as a type of surgical instrument; 1760 as "one who removes scalps," agent noun from scalp (v.).
Meaning "person who re-sells tickets at unauthorized prices for a profit," 1869, American English; earliest reference is to theater tickets, but often used late 19c. of brokers who sold unused portions of railway tickets. [Railways charged less per mile for longer-distance tickets; therefore someone traveling from New York to Chicago could buy a ticket all the way to San Francisco, get out at Chicago and sell it to a scalper, and come away with more money than if he had simply bought a ticket to Chicago; the Chicago scalper would hold the ticket till he found someone looking for a ticket to San Francisco, then sell it to him at a slight advance, but for less than the official price.] Perhaps from scalp (v.); scalper was a generic term for "con man, cheater" in late 19c. Or perhaps the connecting sense is the bounty offered for scalps of certain destructive animals (attested in New England from 1703) and sometimes Indians (i.e., having only part of something, but still getting paid). Some, though, see a connection rather to scalpel, the surgical instrument.