Peel and section oranges over a bowl, reserving juice; place orange sections on a serving plate.
Bring sugar, ginger, 3 Tbsp. water, and reserved juice to a boil in a small saucepan over high heat; cook 2 minutes, stirring occasionally.
Remove from heat; discard ginger.
Pour syrup over orange sections.
Serve with gingersnaps.
Try This Twist! Gingered Clementines: Substitute 4 to 6 peeled and sliced clementines for oranges. Proceed with recipe as directed, beginning with Step 2 (without reserved juice).
Note: Clementines will not have juice to add to the syrup, but there will still be enough syrup at the end of Step 2 to coat fruit.