The story
Blend of Turk + cockroach. Originated from a copypasta on the 4chan board /int/, comparing Turks to cockroaches. Typically used by 4chan users to suggest that Turkish users are annoying and are difficult to rid oneself (or in this case, the 4chan board) of, much like cockroaches.
Etymology from Wiktionary, CC BY-SA 4.0.