Combine the sugar, warm water, and grapefruit juice in a half-gallon jar. Stir or shake to dissolve the sugar.
Add the mugwort leaves and poke them under the liquid so they are completely submerged. Cover the jar with a clean dish towel and set it on the counter to ferment, stirring once a day.
After 3 to 5 days you should notice bubbles when you stir. This is the beginning of fermentation. Continue to stir once a day and start tasting
When the soda is nice and bubbly, strain out the solids and set them aside. Pour the soda into sterilized 1-liter plastic bottles, leaving several inches of headspace at the top.
Leave the bottles at room temperature for 2 days, checking the carbonation level once a day by giving them a quick burp. When they fully carbonated, move the bottle to the refrigerator to stop fermentation.
Spread the solids (grapefruit pulp and mugwort leaves) on a dehydrator sheet and dry until they're brittle. These can be ground as needed and combined with the salt to rim a Primitive Paloma.