How likely is a path to citizenship for an Iraqi refugee without family in Iraq?

The first step would be for this person to be granted refugee status. There is no direct path to citizenship. There is not enough information to assess whether she would qualify for refugee status. Unfortunately, refugee status is not granted to those fleeing conditions of general strife. She must establish a well/founded fear of persecution on account of her race, nationality, religion, political opinion or membership in a particular social group. You can find more information about refugee status at http://myattorneyusa.com/asylum-and-refugee-protection.