Yes, if you and the child meet IRS requirements for doing so. Requirements include: the child must have a social security number and must have lived with you for more than half the year. If some other adult (i.e. the child’s bio parent) claims the child on his tax return, your income must be higher than the parent’s income in order to claim the child on your return.
See the IRS rules here:
For additional related tax questions regarding your foster child, see answer to FAQ #15 here.