Can a husband file for an uncontested divorce without his wife's signature in Georgia?

You can file for divorce without a spouses signature. However, uncontested means that both parties have agreed on the terms of the property settlement and that the court does not need to make the award. For this, you will need a signed Settlement Agreement filed along with your Complaint for Divorce. You cannot do this without her signature.

If she is missing, you may file for divorce, and if she is unable to be located within a certain amount of time, you may serve her by publication. After that, you would have a trial (without her) where the judge would order the divorce and distribute the assets and debt, and order custody/child support.

If she is present and simply refuses to sign anything or agree to the terms you are offering, it is a standard contested divorce.

Answer

yes, but the wife has to be missing (or unable to be located) for a specific amount of time