Yes, you can compost kale.
Even though they’re pretty tough compared to flimsy things like spinach, kale leaves still rot down quickly in a compost heap – the curly leaves stop the heads become too compact so moisture and microbes have an easier job of getting to the heart of the matter compared to things like cabbages.
Stems – of the leaves and the plant if you’ve grown your own – take longer to compost — chop them up into small pieces to speed up the composting process. Don’t forget though, you can eat the stems of the leaves – sliced into thin strips, they’re a fab crunchy addition to stir fries.
In composting terms, kale is a “green” (even the purply ones) so they’re are a good source of nitrogen for your compost heap. If you’ve got a lot to get rid of, stir them in with some “browns” (like newspaper, egg boxes or straw) to keep you compost balanced.