What is the legal ruling for adoption?

The reward of Paradise
Islam encourages sponsoring orphans, rearing them, treating them kindly and seeing to their needs and interests to the extent that the Prophet [peace and blessings be upon him] promised that the person who sponsors an orphan will enter Paradise alongside him.

Evidence from the Sunnah
"The one who raises an orphan and I are like these [two] in Paradise (and he pointed to his middle and index fingers)" [Bukhari].

"An orphan's guardian, whether he is a relative or non-relative, and I are like these two in Paradise" [Muslim].

"Whoever takes in the orphan of two Muslim parents and provides him with food and drink until he can support himself, will enter Paradise" [Ahmed].

"The best of homes in the sight of Allah is that in which an orphan is well treated"
[reported by al-Tabarani from a raised-chain hadith narrated by ibn 'Umar, may Allah be pleased with them both].

"The person who provides for a widow and a needy person is like one who strives for the sake of Allah, and I think he said, "like the person who does not tire of praying and the person who frequently fasts" [reported by Bukhari and Muslim from a narration of Abu Hurayrah, may Allah be pleased with him].

Adoption in Islam
Adoption is taking in another's child as one's own. Islam prohibits adoption and deems all its consequences invalid as attested to by the words of Allah, "… nor does He make your adopted sons into real sons. These are only words from your mouths, while God speaks the truth and guides people to the right path. Name your adopted sons after their real fathers; this is more equitable in God's eyes—if you do not know who their real fathers are [they are your] 'brothers-in-religion' and protégés." [Qur`an 33:4-5]

Allah commanded that whoever sponsors an orphan child is not to attribute it to himself, but to its biological father if he is known; otherwise, the child should be called 'Mawla' or 'brother-in-religion'. In this way, Islam prevents people from changing truths and preserves the rights of heirs from loss or reduction, protects against mingling between the sexes, and being in the private company of a non-mahram [persons to whom marriage is legitimate] such as that between the male adoptee and the maharem [persons to whom marriage is illegitimate] of his adoptive father as well as between a female adoptee and her adoptive father, his sons and male relatives. Such mingling spreads corruption, the evils of which are only known to Allah Almighty who has knowledge of what He created—He is the Ever Kind and All Knowing.

Ruling
Based on this, the responsibility of sponsoring an orphan in Islam includes all the responsibilities and duties of adoption except changing lineage, which Islam prohibits, and its ensuing consequences.

Allah the Almighty knows best.