How much tax will I pay in the state of Georgia on a out of state pension of $1649.00

Depends on your age. GA has an exclusion in its income tax for retirement income of up to $35K if you are age 62, or $100K if you are over age 65. It doesn't matter that the pension is from an out-of-state source.

Even if your age allows the pension to be taxed, the highest rate would be 6%.