Bring the orange juice to a simmer in a medium saucepan.
Meanwhile, rinse the cranberries.
Once the juice is simmering, stir in the sugar.
Once sugar is dissolved, add cranberries. Simmer, covered, until all of the cranberries have burst and mixture becomes thick and syrupy (about 30 minutes).
Taste-test to see if you'd like to add any more sweetener...some folks like a sauce with a little "bite", and others don't, so this just depends on your personal preference. If desired, add more sweetener to taste. Allow the cranberry sauce to cool for at least 15 minutes. It will thicken more as it cools.