Does an exiled Aetherling come back into play untapped?
Yes, when Aetherling returns to the battlefield, it's considered a new permanent, so it enters the battlefield without remembering that it was tapped.


  400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence.
  There are seven exceptions to this rule:


(none of the exceptions apply here).