There are thirteen grounds for divorce in Georgia, the first of which is "[i]ntermarriage by persons within the prohibited degrees of consanguinity or affinity." OCGA §19-5-3(1).
In Georgia, intermarriage is prohibited between the following degrees of relation: father and daughter/stepdaughter, mother and son/stepson, brother and sister (whole or half), grandparent and grandchild, aunt and nephew, or uncle and niece. OCGA §19-3-3(a). Not only are these marriages void from their inception, it should be noted that if a person marries another person to whom he/she knows is related, by blood or marriage, within one of these prohibited degrees, that person is subject to imprisonment. OCGA §19-3-3(a) - (b).
As an aside, you can legally marry your cousin in Georgia. Thus, if you do so and then seek a divorce, you must seek the divorce under another ground, as this relationship is not "prohibited"under Georgia law.