If I am active duty military stationed in Georgia but my spouse worked in the state of Georgia half of the year, Would she file a Georgia state tax return with her W2?

She would normally choose for her state of residence the same as your home of record. So, assuming your home state of record is not Georgia, she would file as a non-resident in Georgia. You will see that option when you start the Georgia tax return in TurboTax. Depending on the rules in your home of record, she may also have to file as a resident in that state. If so, she should get a credit for taxes paid to another state on her resident state tax return if there is any double-taxation of state income.

Your spouse's income may be exempt from GA tax.  See this:

Under the Act, a spouse of a servicemember may be exempt from Georgia income tax
on income from services performed in Georgia if:
1. The servicemember is present in Georgia in compliance with military orders;
2. The spouse is in Georgia solely to be with the servicemember;
3. The service member maintains domicile in another state; and
4. The domicile of the spouse is the same as the domicile of the servicemember or
for 2018 and later taxable years, the spouse of the servicemember has elected to
use the same residence for purposes of taxation as the servicemember.