None of the regular sources list itch as a transitive verb meaning to scratch. Yet I hear it used that way in American English all the time. One of the British mods of this site says the usage occurs in British English as well.
There's even a question on this site about this usage that I myself answered nine years ago, which provides further evidence that such a usage exists.
The verb itself in its main meaning has been in use for at least a thousand years.
Middle English icchen, from Old English giccan "to itch," from West Germanic *jukkjan (source also of Middle Dutch jöken "to itch," Old High German jucchen, German jucken).
Given that itch meaning to scratch appears now both in AmE and BrE, there must be some logical progression to the transitive usage. What I want to know is how (and possibly when) this usage came into being. Is it because itch ends on the same phoneme that scratch does? Is it baby talk that gained currency?