No, they do not correct astigmatism. Only prescription lenses can do that. Non-prescription blue light glasses simply filter light, so they will not sharpen the blur that astigmatism causes. If your vision is fuzzy, a blue light filter on its own is not the fix you are looking for.
The good news is you can combine both. Many opticians add blue-light filtering to prescription lenses, or you can wear non-prescription pairs over contacts. For actual correction, see an eye doctor. For screen comfort on top of that, a filtered lens can still earn its place.