Rinse the cranberries under cold water and pick out any stems or debris. If using frozen cranberries, there is no need to defrost them, but you may need to adjust the amount of cooking time to account for the extra liquid.
In a medium saucepan, combine the cranberries, sugar, and orange juice.
Heat the mixture over medium heat, stirring occasionally, until the sugar dissolves.
Add the orange zest and cinnamon stick to the saucepan. The orange zest adds a bright citrus flavor, and the cinnamon stick adds a hint of warmth, but feel free to omit them if you prefer a more straightforward cranberry flavor.
Bring the mixture to a boil, then reduce the heat to simmer. Let it cook for about 15-20 minutes, or until the cranberries burst and the mixture thickens.
Stir the jam occasionally to prevent it from sticking to the bottom of the pan.
Remove the cinnamon stick and let the jam cool for a few minutes.
If you prefer a smoother jam, you can use an immersion blender to puree the mixture to your desired consistency.
Transfer the cranberry jam to sterilized jars, leaving a little space at the top. Seal the jars and let them cool to room temperature. This recipe typically yields about 1 pint of cranberry jam.
Once cooled, store the jars in the refrigerator. The jam will continue to thicken as it cools.