When people ask a question like this, I like to think to myself "what would happen if this were actually possible?" I don't really know what this would mean, but I guess it would have something to do with being able to override the constructor implementation based on the dynamic type of the object being created.
I see a number of potential problems with this. For one thing, the derived class will not be fully constructed at the time the virtual constructor is called, so there are potential issues with the implementation.
Secondly, what would happen in the case of multiple inheritance? Your virtual constructor would be called multiple times presumably, you would then need to have some way of know which one was being called.
Thirdly, generally speaking at the time of construction, the object does not have the virtual table fully constructed, this means it would require a large change to the language specification to allow for the fact that the dynamic type of the object would be known at construction time. This would then allow the base class constructor to maybe call other virtual functions at construction time, with a not fully constructed dynamic class type.
Finally, as someone else has pointed out you can implement a kind of virtual constructor using static "create" or "init" type functions that basically do the same thing as a virtual constructor would do.