It's not a perfect replacement for AppleCare in that it doesn't include service or access to Apple repairs, but it's something that's already included in many credit cards, and might be just the ticket for you. Here's what you need to know.
Firstly, be sure and check your bank's credit card features to know what you have. We aren't ripping off Magnify Money's list, so check their article for the full list and links to the bank. Secondly, you don't have to purchase your iPhone with a particular credit card for this coverage, you have to pay for your service with the card to get the coverage.
Magnify Money has a list of some 26 banks, but 18 of them cover you for $200, and five of them cover you for $250. Hancock Bank and First Citizens Bank will cover you for $500, and Wells Fargo will cover you for $600. And that's up to twice a year.
The coverage works like this: if your device is damaged, you send it in. The third party company your bank uses will fix the device. If they can't, the service will pay for a replacement directly from your carrier's online store. You're on the hook for the balance above what's covered. There's a small service fee per incident, too.
Check with your bank on its policies for a stolen phone.
As I noted, this isn't a perfect replacement for AppleCare, but for those cards with Cellular Telephone Protection, it's free.
One last note: Magnify Money is an infinitely scrolling website, and I found it pretty easy to jump to another article without realizing it, especially when doing a find. You may need to use the click-and-hold on your browsers back button to get back to the right article. Even there I sometimes had to reload once I got back to the proper URL. Otherwise, come back to this article and click the link anew.
Broken iPhone image courtesy of Shutterstock.