No.
Only the person that paid the childcare can deduct it.
The child doesn't have to be your dependent, but the child must live with you. Only the custodial parent can claim the child care credit. And to claim the credit, the person claiming the expense must have paid it. To be your qualifying child for this credit, a child must live with you for more than half the year and meet other requirements.
Please see this link: https://www.irs.gov/publications/p503/ar02.html#en_US_2015_publink1000203265
