Turn the smart guides on (Ctrl + U) and drag the anchor point to the center of the object until it says "center". From the Attribute panel you can show the center point of selected objects.
the anchor point
the horizontal and vertical centre
The object that the Anchor Point belongs to may be aligned with other objects in various ways including by its centre without anything being there.
I think you must mean Centre Point (which isn't an anchor).
It is in the centre of an object's rectangular bounding box and therefore not necessarily in the geometric centre of the object itself.