Yes, if you don't over do it.

There is a chemical in the rind that it toxic to worms. As the rind decomposes, this chemical breaks down, and the worms have a feast. Treat the oranges like any other questionable item you put in the bin. Put a small amount (half of an orange?) in one corner of the bin and see how the worms respond. When I tried this, the worms were all over the oranges in just a few days.

If you grind your worms' food, you can mix in some of the orange. It will break down quickly, and you will hardly know that it is there.

Suggestion: slice oranges, simmer in hot water... pour water out over weed patch [weeds between pavers?] When making candied orange peel, this is repeated 3 times ... I'm guessing that a similar treatment for these old oranges .... followed by grinding in the blender, will leave only good worm food...... a bit of work, but -... well, you know.....