Unfortunately, you cannot claim her for child tax credit as one of the requirements for the child tax credit is that you must claim her as a dependent.
A future note (FYI): As a US citizen, when she gets older, she will have a US filing requirement annually to declare her worldwide income if she meets the requirements for filing a US tax return. In 2017 for someone single, she would need to file a US return if her income was over $10,400 ( which is the sum of the 2017 standard deduction for a single taxpayer plus one exemption.), or if she had net earnings from self-employment income of at least $400. US citizens that live abroad have the benefit of the foreign earned income exclusion and the foreign tax credits to help offset double taxation.
Please see the following IRS publication for more information:
Tax Guide for US Citizens Abroad
