Want a free case for your faulty iPhone 4? There’s an app for that!

Making good on its promise last week, Apple is now beginning to accept orders for free iPhone 4 bumper cases, but you have to submit them through an app on your iPhone 4.

There is a new app in the App Store called “iPhone 4 Case Program.” It prompts users to sign in with their Apple ID, which will verify that they have an iPhone 4, and from there it’s a piece of cake: choose your color and manufacturer and it’ll be on its way.

Apple says it will take three to five weeks to send out the cases.

For those who purchased a bumper in the draconian “no free bumper case!” days, anyone who bought it with a credit card on Apple.com or an Apple Store will receive (and might have already received) a refund automatically.

Those who bought a case from the Apple Store with a cash, check, or gift card can take their original receipt into the store to get an immediate refund. If you used a gift card on Apple’s website, a new gift card will be sent out.

Anyone who purchased a case from an AT&T store will have the most difficult time. Those people need to fill out a special rebate form, include a copy of the receipt, mail it in and wait.

Although the offer of a free case to reduce the antenna signal problems was long overdue, at least now that it is here, Apple is making it relatively painless for everyone.