Is it permissible to give a vow to one's poor, needy father who is in debt?

If you did not intend a vow with the promise you made, then nothing is binding upon you. However, if you intended a vow along with uttering the promise or a صيغة (formulation) that implies commitment, then you are obliged to fulfill it once the condition it is contingent upon is met. It is permissible to disburse the vow to pay off an indebted parent's debt, because the debtor is one of the recipients of Zakat, and a vow is disbursed to the recipients of Zakat. Zakat is given to the debtor if their debt is for a permissible matter, not a forbidden one.