Were Christians in the Roman Empire known to rescue abandoned babies?

I've read in a Christian publication that one of the things that distinguished early Christian groups in the Roman empire was that they would rescue babies that had been abandoned by their parents. In Rome, it was considered acceptable to abandon a newborn to the elements if the family (specifically the father) decided not to raise it. Allegedly, Christians would collect these infants and raise them in their community. What are the sources for this claim, if any?