Origin of rung2
Word Origin for rung
Old English hrung "rod, bar," from Proto-Germanic *khrungo (cf. Middle Low German runge, Old High German runga "stake, stud, stave," German Runge "stake, stud, stave," Middle Dutch ronghe, Dutch rong "rung," Gothic hrugga "staff"), of unknown origin with no connections outside Germanic. Sense in English narrowed to "round or stave of a ladder" (first attested late 13c.), but usage of cognate words remains more general in other Germanic languages.
This [rungs] has generally been considered as a mere corruption of rounds; and people of education use only this latter word. [John Pickering, "A Vocabulary or Collection of Words and Phrases which have been Supposed to be Peculiar to the United States of America," Boston, 1816]