Heat a cup of water in the microwave or on the stovetop until hot enough to dissolve the sugar and salt but not boiling. Remove it from the heat and pour in the salt and sugar, stirring until they dissolve.
Add the remaining water and apple cider to cool the brine. It should not be warm—you want it completely cooled.
Put the chicken wings in a non-reactive pot or glass container and pour the cooled brine over them. Add the garlic, thyme, bay leaves, peppercorns, pepper flakes, orange slices, and lemon slices. Then, cover the pot with a lid or plastic wrap and brine it in the fridge for 45 minutes to an hour. Wings are small, so try not to let them brine for over an hour.
Remove the chicken wings from your brine and pat them dry with paper towels.
Brush with butter and rub with your favorite seasoning. You're now ready to grill, bake, or smoke your wings.