The common understanding of what oracle does is that it answers a question after a single operation.  So at first glance, it runs in $O(1)$.  But, doesn't it need to actually read the input?  Wouldn't this take at least $n$ steps?  If so then wouldn't an oracle run in $O(n)$?
Do Oracles run in O(1) or O(n) time?
complexity theory;time complexity;oracle machines