Diatomaceous Earth and Boric Acid (found in Borax Mule Team laundry detergent) both have the same effect on ants and both work without doubt. When an insect comes into contact with the them, it sticks to the insect and literally shreds its exoskeleton. The insect dehydrates and dies within hours.
If your cats are indoor/outdoor, let them out, take a fine strainer and sprinkle either of them all over your carpet especially along the edges of rooms. You can walk on it, shake it in, get it nesteled in carpet fibers, etc.
If you use Boric Acid, then vaccuum with a light setting so your cat's don't get too much of it on them and lick it while they're cleaning. Don't freak out - they'll be fine. I've used Borax in the past three times this way and it always works like a charm. Enough of it settles so it doesn't get vaccuumed up to do the job.
You could mix either with some cinnamon powder which is a deterrent.
You can also sprinke them right around the perimeter of your house. Do so on a calm (not windy) day when you know you'll have a few dry days before it rains.
If you choose Diatomaceous Earth (ground up seashells) you can use a skimmer to apply since it it's finder than baby powder. Sprinkle close to the carpet and edges, not from waist level. You want it to get to the surface as quickly as possible because you don't want it floating around in the air. As long as it's not in the air, Diatomaceous Earth is harmless to your cats.
Any bug that has a hard exoskeleton including fleas and roaches are vunerable to boric acid, and they cannot grow immune to it either like they can to other pesticides including Permithrin.