E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Aroint thee.
Get ye gone, be off. In Cheshire they say, rynt ye, witch; and milk-maids say to their cows when they have done milking them, rynt ye, (or roint) my beauties; but it is doubtful whether this is connected with the word in question.