Vinegar can sometimes deter ants, but it takes a lot, and my cat despises the smell. She growls now every time I bust out the vinegar spray bottle.
I recently tried Ortho Eco-Sense Indoor Insect Killer in my doorway/kitchen/porch area, as I had the same problem with ants, and it worked like a charm. It really does kill bugs on contact. It's supposed to be naturally-based, and claims to be safe for pets, though it does leave oily marks for a while and it has a strong smell when used in a confined space (my small kitchen!), so I would make sure the cat can't get to it until it's all cleaned up. I found the stuff at WallyWorld (Walmart) in the gardening/organic section, and it's not terribly priced. I think I paid $4.50 for one bottle.