"to produce smoke," see smoke
(n.). Meaning "to drive out or away or into the open by means of smoke" is attested from 1593. Meaning "to cure (bacon, fish, etc.) by exposure to smoke" is first attested 1599. In connection with tobacco, the verb is first recorded 1604 in James I's "Counterblast to Tobacco." Smoking gun
in figurative sense of "incontestable evidence" is from 1974.