> Drag, drug, druggen/drawn. Some of these may not be current in your dialect anymore. I say dragged.
"Drawn" also only really feels right for the passive voice. For using "drawn" actively, the only thing that sounds remotely right is "I drew", but that sounds super strange compared to "I dragged", I'm not even sure I would have recognized the former as a usage of the verb "drag" before thinking about all this.
Draw is closely related to drag, and draft. Draft animals that draw are dragging, at last by the dictionary definitions, though it is a little archaic sounding. Draw is dragh. The written "gg" is sometimes reduced to "gh" in Middle English between two vowels of the same closeness. Similar to the "ch" sound of German. It sort of swallows it, or reduces it to a fricative. So draggan -> draghn -> drawn. But only in some dialects. A whole cluster of related words. Also in this series is drive, draft. For some reason, it's a tendency for f and gh next to a /t/ to swap out. They do sound pretty similar, I suppose. The British still spell draft as draught.
Old English has: dragan -- ic drage, he drægþ (dragth), ic drog/droh, he drog/droh. Dragende, gedragen.
Standard Modern English has: to drag -- I drag, he drags, I dragged, you dragged. Dragging, dragged.
Variant there's also: to drag -- I drag, he drags, I drug, he drugs. Dragging, drug/drawn/druggen.
"Drawn" also only really feels right for the passive voice. For using "drawn" actively, the only thing that sounds remotely right is "I drew", but that sounds super strange compared to "I dragged", I'm not even sure I would have recognized the former as a usage of the verb "drag" before thinking about all this.