I've done a good bit of surfing adoption agency websites in my online life. I've seen a fair number of agencies use a religious belief to promote adoption; quoting particular scriptural passages is a common way to do this. The ones I see most frequently come from the New Testament of the Bible: Romans 8 , Ephesians 1 and Galatians 4.
These are by no means simple passages; they speak to God's spiritual adoption of humanity. This concept of biblical or spiritual adoption, and the most appropriate translation of the original Greek word often translated as adoption, huiothesia, are both subjects of considerable scholarly discussion. Add to this the historical context for adoption in Greece, Rome and Israel at the time the Bible was written, and it becomes arguable at least that God may have had something other than modern-day adoption in mind in these Pauline letters.
It's tempting, though, to seek one's personal convictions to a particular passage of a particular religious document. Finding words that raise our deepest convictions and desires to the level of God's word is comforting and inspiring. No doubt this is why these particular texts get so much attention in the adoption community. But there's risk, however, that seeing this one message in these texts, in spite of the fact that this may not be the right message at all, may send us down the wrong adoption path, and may even cause us to miss deeper, more subtle message.
It is just my opinion, but I think there's a much stronger message about adoption in the Bible, in Matthew 22:
Loving like this opens our eyes to the pain our own actions may cause others. When we look at adoption through this lens, and think about it from the perspective of our neighbor - our child, for example, or our child's mother or father - our attention will naturally turn to practicing adoption appropriately and making it ethical and just. I think that would be very pleasing to God indeed.
You shall love your neighbor as yourself.
Interesting reading on the historical context of adoption in ancient Greece, Rome and Israel:
Jacob Adopts Ephraim and Manasseh
Marcus L. Burstein
The Cambridge Dictionary of Classical Civilization
Scroll down to the sub-heading adoption