Is the child tax credit based on your earned income?

If you are specifically speaking of the Child Tax Credit and not the Additional Child Tax Credit, then the credit is generally $1,000 per qualifying child, with limitations for high income taxpayers AND for the amount of tax you owe. That is, if your tax initially computes out to be only $500, then the Child Tax Credit is limited to that $500. This is because the Child Tax Credit is a non-refundable tax credit, that can only reduce your tax to zero.

The Additional Child Tax Credit is computed differently, and comes into play when you can't get your full $1,000 per child because your tax was reduced to zero before the initial $1,000 per child was used up.

For additional reading, please see https://www.irs.gov/uac/about-schedule-8812-form-1040