I see nothing in Scripture that would prevent single Christians from adopting children from Third World countries. Though it is best for children to live in a healthy family where there are a mother and a father, sometimes single-parent adoptions can work, and a single-parent home in America could easily be better than living in some of the deplorable conditions found in some Third World countries. I just don’t see any blanket statement saying it is always right or it is always wrong for single Christians to adopt children. Nevertheless, we have to look at each circumstance on its own merit.
However, not all Third World country situations are bad. I have been to the hill-country in the Philippines and saw destitute people living in what we would call shacks. But, the children seemed happy, fed, and loved. Nevertheless, it is a good and loving thing to want to care for children who are in bad situations – provided they really do need our help. If they’re in orphanages, on the street, don’t have parents, and things are generally bad for them, it would certainly seem good for Christians to adopt them and take care of them. If that means that a single Christian is the only one available to do it, I think it’s better than leaving them in dire circumstances.