This is from the IRS website: Topic No. 602, Child and dependent care credit
Children of Divorced or Separated Parents or Parents Living Apart - A noncustodial parent who is claiming a child as a dependent should review the rules under the topic Child of divorced or separated parents or parents living apart in Publication 503PDF, because a child may be treated as the qualifying individual of the custodial parent for the child and dependent care credit, even if the noncustodial parent is entitled to claim the child as a dependent.
If your child lives with you, you are the custodial parent, then you should be able to claim the dependent care credit.
