Combine the water, cider, brown sugar, salt, peppercorns, bay leaves, garlic, orange strips and rosemary leaves in a large pot. Stir until the salt and sugar dissolve. Bring to a boil, and then turn off the heat and cover. Allow to cool completely, and then place into the fridge to chill.
Place an uncooked, fresh turkey in the chilled brine solution, and then refrigerate for 16 to 24 hours. (You may add more cold water if you need more liquid for the size of turkey you have.)
When you're ready to roast the turkey, remove the turkey from the brine. Submerge the turkey in a pot or sink of fresh, cold water. Allow to sit in the clean water for 15 to 20 minutes to remove excess salt from the outside. Discard the brine.
Remove the turkey from the water, and then rinse again, pat dry and cook according to your normal roasting method.