Charitable Contributions are claimed on Schedule A , as itemized deductions.
TurboTax starts off using the Standard deduction, so until your Itemized Deductions are higher than the Standard deduction your refund would not change. Or it will just change a little at a time as you increase your deductions over the standard amount. Note - Your donation does not count "dollar for dollar", it is calculated by a percentage based on your tax bracket.
Please see TurboTax faq instructions below on where to enter Charitable donations: