Given that much of the English speaking world has had unlimited calling plans, partially unlimited calling plans (e.g. the "Fave Five"), or at least very cheap "minutes" for quite some time, I suspect that most people wouldn't know a term for this — I certainly didn't. However, I was able to find some older terms in an article (Sweethearting, part 2, from 2005):
I received reports of pranking being used all over the world. It’s called one-belling (or pranking) in England, people send “toques” (roughly “touches”) or “sting” each other in Spain, Italians “fare uno squillo” (which Google translates as “to make one blast”), and in Finland it’s called “bombing”.
Update: In South Africa, they call it a “Scotch call”.
One Bell
To telephone someone and let the phone ring once before hanging up. Usually done when the onebeller is low on credit.
"I haven't got much credit, so I'll one bell you when I get there and you can call me back, yeah?"
— Urban Dictionary, 2009
Scotch call
Partridge defines "scotch call; scotch ring; scotchie (noun)" as South African. "Scotch call" in quotes is used in this patent by a South African man. Unfortunately, it doesn't have great connotations:
A “Scotch call” implies Scots are stingy, referring to hanging up before the other person has answered the phone
— ECAJ Antisemitism Report
Pranking
As for "pranking" I found a post on the Everything2 forums:
In Australian youth slang, to prank someone means to dial their mobile phone, then hang up before they pick up.
It does not necessarily mean doing so in a malevolent way; rather it is a way to avoid exorbitant mobile charges when a person picks up; since phone companies do not charge if the receiver does not answer.
It is used as a verb, e.g., "I'll prank you when I get to your place and you can come down."
From a Facebook comment on a post mentioning supposedly untranslatable words like "Prozvonit (Czech): To call a mobile phone and let it ring once so that the other person will call back, saving the first caller money."
'prank' is used this way: "I've got no credit, so I'll prank you when I've got that information."
Also backed up by Duckspindle in the comments here on ELU:
I first came across the term 'pranking' in about 2000. My teenage daughter said she would prank me when she arrived safely. When I asked what she meant, she said that she would let the phone ring then hang up, 'like people do with prank calls'. It was a common method of passing a pre-arranged message when each call was charged for - let the phone ring three times and hang up. The recipient would then do the same. If either party didn't hear the three rings, a voice call was in order. I'm not aware of any name for the practice before 'pranking', and these days there is little need for it.
Flash [Call]
Through Wiktionary I also found to flash:
(transitive) To telephone a person, only allowing the phone to ring once, in order to request a call back.
Susan flashed Jessica, and then Jessica called her back, because Susan didn't have enough credit on her phone to make the call.
(Not to be confused with Wiktionary's definition #5 for flash, which is lewd but also transitive.)
Less ambiguously, flash call:
When we had cell phones it was called “beeping.” Now in the era of smartphones another word serves better. It’s “flashing” or “making a flash call.” I think we even did it with land lines as well back in the day. Children away from home would flash call their parents. Though we didn’t recognise it as a thing then.
To make a flash call is to send a message to someone for free simply by calling them up on your phone. Then you (the caller) hang up before the other person gets round to answering the call. As long as the party you are phoning doesn’t pick up the call then you have at least gained their attention without having to pay for a call. That’s a flash call.
Africa calling: How to say a lot with a little
