setFixedAnchor is indeed defined on InfoWindow. The popup does not have this method.
What are you trying to change about the default popup positioning? As is, the popup always positions itself within the map.
Is there any way to assign where the anchor is located, as ANCHOR_LOWERLEFT can with InfoWindow?
No, there isn't a way to do this. The popup will do its best position itself within the map (and this works, as long as the popup isn't bigger than the map container). If you always used ANCHOR_LOWERLEFT, there's a good chance you could be opening the popup but it wouldn't be 100% visible, which would then require to pan to see all of it.
If I'm missing something, can you post some screen shots that show what's happening now and perhaps mock-up what you'd like to be happening?