Am I permitted to give money as charity to those under my care?

It is permissible to give Zakat to someone whose expenses you cover gratuitously, such as an orphan who is not an heir, because there is no text or consensus prohibiting it. This is also supported by the Prophet's (peace and blessings be upon him) statement to Ibn Mas'ud's wife when she asked him about giving her Zakat to her brothers' orphans under her guardianship: "Yes."