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Just as there are differences of belief about the nature of Christ, there are some different ideas about this in some branches of Christianity. However the mainline orthodox belief has a pretty settled answer to this: yes.
Assuming ⓐ the trinity, one God in three persons and ⓑ that Jesus was God the son having two complete natures, the logic goes something like this. Different branches of Christianity use different terms for some of this, but the basic argument is the same.
Ergo the divine nature of God must have been subjected to and born the divine wrath side of things.
I question some time ago that asks about the same problem from a different angle, see How is Christ's death so significant? for a little more detail on the significance of “one man on a cross”.