Parent to bone (by only rotation), or snap head to origin of other object I'm creating a model with many separate moving parts. 
As shown in the image my bone rotates the part according to the bones axis.

Is there any way to snap the bones head to the position of said parts origin, so it rotates on it's own axis?
If I understand your question, you want to build an armature (in edit mode) in which the bone's head is exactly in the object origin location. To do so, select the object, press Shift S (Cursor to selected), then select the armature, go to edit mode, select the head of the desired bone, press Shift S (Selection to cursor). THEN parent the object to the bone (Ctrl P - Bone).