Foster children are on the one hand a part of the household but on the other hand not legally adopted and may be ultimately reunited with their birth parents. So do Presbyterians of a confessional variety, like PCA or OPC, baptize foster children?
I don't think any denominational body has ruled on this; until one does so, it remains a matter of conscience for individual believers. Part of the difficulty is that foster care as a named/organized phenomenon only goes back to the 19th century.
That said, there seem to be two main schools of thought: yes and no. End of answer. I'm kidding... but those are the main schools of thought.
As this answer explains well, two of the key concepts regarding paedobaptism are 1) that baptism replaces circumcision in the new covenant, and 2) that the command to baptize is issued to "you and your household/children." So arguments about whether or not to baptize foster children rely on applying these two concepts.
The real rub is, can they be rightly called the children of their foster parents?
Those who argue against baptizing foster children point out that baptizing one's children involves a commitment to rearing them in the ways of the faith; in most reformed congregations, both the parents and the rest of the congregants take vows to the effect that they will instruct the children in the faith. The key question posed by those opposed to baptizing foster children is: can you truly make such vows?
But this can be countered by pointing to the old covenant example. All male members of the household were circumcised: children on the eighth day, and slaves (and whoever else) as soon as possible. But slaves were not necessarily a permanent part of the household; if they were circumcised and left the household, they would still be covenant members. In the same way, foster children could be temporary members of the household while being permanent members of the covenant. While a part of the household, the parents bear responsibility to instruct them in the faith, just as they vowed to do.
I'm not advocating either position. I suspect that if you were to ask a representative of any of the large Presbyterian denominations what to do, they would say, "Discuss it with your pastor." It probably demands close attention to the specific situation, as well as prayer.
I asked this question when I was first exploring becoming a foster parent. Three years later, I have had two foster children both of which remained unbaptized while in our care.
Because a Presbyterian view of baptism is that it is the sign of covenant membership. Since foster children are not legally and covenantally permanent members of the family prior to their adoption, it would probably be theologically out of order to baptize the child since it would not be possible to uphold the vows to raise the child as a Christian family since if the courts decide, the child may ultimately be reunited with parents or adopted by other caretakers. As members of the household, they are still raised under the Christian care of the family and the church. They are just temporarily member in limbo, waiting to achieve permanence.
Incidentally, it is also illegal in the US for foster parents to have a foster child baptized apart from the child's consent or the parent's.