I have made orange sorbet many times and yes, it is possible to make sorbet without a sorbet or ice cream maker. The only tool you need is a food processor. Whenever I am lazy (which is most of the time), I cheat with 100% pure orange juice to save myself the hassle of juicing.
You can use any brand of orange juice, as long as it is pure orange juice, meaning there is only one ingredient – “(pasteurized) orange juice”. The brand that usually sits in my fridge is Florida’s Natural (No Pulp) orange juice. I also added lime juice to balance the sweetness of the oranges and to provide a subtle lime citrus aroma. This is the perfect recipe to beat the heat, or to use up lots of leftover oranges (including tangerines and mandarin oranges) quickly.