Yes*.
Enter her information in the personal info section of TurboTax (TT) and follow the interview. Since she is under 17, she will qualify you for the (up to) $2000 Child Tax Credit and maybe the Earned Income Credit.
The child tax credit (CTC) is limited to your tax liability. The CTC is a non-refundable credit and can only reduce your income tax to 0, It can not help you beyond eliminating your tax liability. But, if you have more than $2500 of earned income, some or all of it is usually given back to you thru the "Additional Child tax credit". That is, part of the CTC may be on line 28 of form 1040 (2020 version) instead of line 19 (lines 18b and 13a in 2019). The ACTC is calculated on form 8812 and is basically 15% of your earned income over $2500. The ACTC is a maximum of $1400 per child (not $2000).
*A child closely related (great granddaughter counts) to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:
See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html
How do I answer the question concerning relationship?
The child can be your dependent under either of two rules. Firstly, because she is a direct descendent of you (a child of your granddaughter) you could claim her if she lives in your home for more than six months even without a court order. Second, the court placement makes her a foster child which also gives you the ability to claim her as a dependent under the foster child rules.
@dboulian wrote:
How do I answer the question concerning relationship?
Either "foster child" or "grandchild" will be fine. (I believe Turbotax includes the option for grandchild, it is the same for tax purposes as great-grandchild.)