Can one citizen swear out a criminal warrant against another citizen in Georgia and if so, what is the process?

This site has the information that you need. You cannot just go down to a courthouse and say that you want someone arrested. This site explains the process. It is specific to Taliaferro county, but cites the GA constitution, so you can apply it to your location.

It is not really a "citizen arrest" although you can do that also for a felony that is in process. For example if the bank was being robbed, you could stop the robber and "arrest them" but in doing so if you detained them, you open yourself up for law suit and possible arrest if you were wrong.

A security guard for example is using a form of citizen arrest in Georgia when they hold someone for the police.

If you want to file charges, first you call the DA and try to have them, if they will not, you can file a complaint, the other person is served to appear in court and you appear to present evidence to show a crime happened and that there is enough evidence to show the other person did it. If the judge believes this is true and there is enough evidence, they will issue a warrant and charges for this.