“‘Happy are they that keep justice, that do righteousness at all times’ (Psalms 106:3). Our sages ask: Is it possible to do righteousness at all times? ... Rabbi Samuel ben Nahmani said: This refers to a man who brings up an orphan boy or girl in his house and enables them to marry” (Talmud Ketubot 50a).
While there is a specific mitzvah/commandment given to all men to be fruitful and multiply (p’ru u’rvu), the sages noted in Talmud Megillah 13a that “whoever raises an orphan boy or girl in his house, Scripture considers it as if she/he gave birth to him/her.” Adoption or foster care, therefore, is certainly encouraged by Jewish law.
When adopting a Jewish child, it is particularly important to have as much information about the biological parents as possible because, according to Jewish law, a person is only halachically Jewish if his/her mother is Jewish or if one formally converts. This information is usually requested when the child seeks to marry or for other life-cycle events.
Adopting a child born of Jewish parents, however, is often not possible (due to lack of availability), and halacha (Jewish law) fully allows for the adoption of a non-Jewish child. When such an adoption occurs, the child undergoes conversion as a minor, which includes circumcision (for boys) and a visit to the mikveh (for both boys and girls) before a Beit Din (Jewish court). The child is then raised as a Jew. However, because a small child cannot really comprehend the conversion process, at the age of halachic adulthood (bar or bat mitzvah), the child must reaffirm his/her desire to be Jewish in front of a Beit Din.