Divorced is not a filing status for an income tax return. If you are not married, then you file as Single, unless you happen to have a qualified dependent that allows you to file as Head of Household. The software asks if you are divorced in order to navigate you to the correct filing status, but your Form 1040 will allow you to file as Single, Married filing jointly, Married filing separately, Head of Household, or Qualified Surviving Spouse.
Divorced is not a filing status, it is only used to determine whether you should be filing as Single or Head of Household.
If you are not legally married and do not have a qualifying person as a dependent then you would be filing the tax return as Single.
Turbotax asks the question to be more user-friendly, so that someone who is divorced will not be confused if "divorced" is missing. Turbotax will put "single" on the actual tax return, whether you select single or divorced.
Divorced is a marital status, not a filing status. TurboTax asks for your marital status so that it can ask appropriate questions. You should select Divorced. It might affect what questions TurboTax asks you later on. If you pay or receive alimony you should definitely select Divorced. After you enter some more information, TurboTax will select the appropriate filing status for you.