Vatican City does not have a general immigration policy for immigrants, as it is not open to mass migration like other countries. Citizenship and residency are granted almost exclusively to those who perform official duties for the Holy See or the Vatican government, such as clergy, Swiss Guards, and their families. While Pope Francis has supported settling refugees with communities elsewhere, they are not settled within the Vatican's walls.
Pope Leo, tear down those Vatican City Walls! (ironically built by the order of Pope Leo IV)