The scheme works by calling phone numbers, letting them ring once, and then disconnecting. The call lasts just long enough to register on your phone's Caller ID, but is short enough you likely won't be able to answer. If someone is curious enough to call back — and that's what the scammers are counting on — they're hit with international calling fees, as well as steep per-minute charges.
I got one of these calls on my iPhone and didn't answer or call back. My rule of thumb is if I don't know the caller, and they don't leave a message, then it isn't important enough to follow up.
Getting calls you don't recognize from Antigua? It's probably scammers
A little Internet sleuthing turned up a Better Business Bureau article calling this the “One Ring” scam. According to the BBB, victims find a US$19.95 International calling fee on their phone bill, plus $9 a minute or higher charges for the call. The scammers use tactics like playing hold music to keep people on the line longer, racking up even more charges.
The bad news is it's far too easy to call back, and scammers are targeting everyone they can, not just iPhone users. The good news is that phone companies are aware of the scam, so a call to your service provider should keep you from a big surprise on your next phone bill if you did succumb to curiosity can call back.