Mix dried cranberries with juice and sugar, and bring to a boil over low heat. Let it simmer without the lid for about 15 minutes.
Wash the orange with hot water and dry. Grate 1 T from orange peel and squeeze out juice. Remove cranberries from heat and stir in orange juice and zest. Let it cool. Puree the mixture, pour into a cold-resistant bowl and place in the freezer.
After one hour, stir the mixture well and put it back into the freezer. Repeat this process 2 to 3 times. Remove sorbet from the freezer about 15 minutes before portioning and serving into chilled glasses.