No. Foster Care Payments received from an official child placement agency, such as a state or local government, are not considered taxable income, and do not need to be reported on your income tax return in any way. Neither are they deductible from your otherwise taxable income.
The reasoning here is that the foster care money you receive from the government is primarily intended for the direct support of the foster child, and is not intended as income (profit) to the foster parents.
Hopefully that answer and brief explanation makes sense. Thanks for asking this important question!