If I do not have any earned income (my income is exempt) do I still file for taxes? If so, can I still get the child tax credit for my child without having any income? This is the first year I have been out of work so I do not know what to do.

If your income is exempt from taxes, then the Child Tax Credit does not apply to you. You MUST pay taxes to get that credit.

No you can not file income tax if you have not work but you can pay taxes.