Cranberry Juice should not make you constipated since Cranberry Juice contains a certain amount of fiber in both the cranberries and cranberry juice.
Drinking too much Cranberry Juice can cause you to have an upset stomach and Diarrhea but it shouldn't cause constipation.
In fact the Cranberry Juice should relieve Constipation if drinking enough of it.
Even Cranberries can help to get your bowels moving and relieve constipation.