Maybe. The Child and Dependent Care credit goes on the tax return of the parent who has primary custody, regardless of who is claiming the child as a tax dependent. Even if your ex is claiming him as a dependent, you would add your son as a nondependent under Personal Info. Indicate that the child lives with you, and also indicate that you are not claiming him as a dependent. Then you can add the child care.
If the child does live with you more than he lives with his father, make sure his father doesn't indicate primary custody on his tax return. Claiming the child and custodial benefits are 2 separate issues.
If the child lived with both of you equally, the parent with the higher AGI would claim the custodial benefits.