All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
In principle adoption is forbidden as it may lead to the mixing of the family lineage and losing some rights, like inheritance and the like. In addition to this, the adopted son may happen to be in seclusion with the girls of the person who adopted him; this applies also to a person who adopts a girl. Therefore, if it is safe not to commit such prohibitions, and the matter is just to help the one being sponsored (yourself) obtain his visa, and there is a dire necessity or need for what is mentioned, then we hope that this is permissible.
For more benefit, please refer to Fataawa 86418 and 86193.
Allaah Knows best.