Yes, assuming that you already meet the other requirements to claim the child care credit, but are missing the required ID number of the provider, you can still claim the credit by demonstrating "due diligence" in attempting to secure the needed information.

When the care provider refuses to give the identifying information, the taxpayer can still claim the credit and is instructed to provide whatever information is available about the provider (such as name and address) on the form used to claim the credit Form 2441 (PDF), Child and Dependent Care Expenses, or Form 1040A, Schedule 2 (PDF), Child and Dependent Care Expenses for Form 1040A Filers). The taxpayer should write "see page 2" in the columns calling for the missing information. He/she would write at the bottom of page 2 that the provider refused to give the requested information. This statement will show that the taxpayer used due diligence in trying to secure and furnish the necessary information.

References:

• Form W-10 (PDF), Dependent Care Provider's Identification and Certification
• Form 2441 (PDF), Child and Dependent Care Expenses
• Form 2441 Instructions, Child and Dependent Care Expenses
• Publication 503, Child and Dependent Care Expenses
• Tax Topic 602, Child and Dependent Care Credit

Source: www.irs.gov