There isn't a number of rings setting. There is a time setting with a time limit - I believe the time limit is 30 seconds, which can be changed by AT&T for your line/number. Keep in mind that the time may start at the server before you get the first ring depending on network connections at the time, etc.
How to change how long your iPhone rings before calls go to voicemail
I had changed this setting on a previous phone years ago and wanted to make sure I had the longest setting possible on my iPhone since it sometimes takes me a while to dig it out of my purse. I can’t take full credit for these instructions, having found them on an old Cingular users forum, but I have updated them to be specific for the iPhone on AT&T.
You can choose between 5 and 30 seconds in increments of 5 (5, 10, 15, etc.). I haven’t tried anything longer than 30 seconds. I have confirmed that this works by setting it for 30 seconds, then 10 seconds, then 30 seconds, and testing it each time by calling my iPhone and timing how long it rings before going to voicemail.
First, you’ll need to know your voicemail access number. The easiest way to get this is to dial *#61# and then press Call on your iPhone’s keypad. The first block of text you’ll see on the screen that comes up will be:
Setting Interrogation Succeeded
Voice Call Forwarding
When Unanswered
Forwards to +1XXXXXXXXXX Enabled
Where +1XXXXXXXXXX is shown as an actual number - write this number down because you’ll need it in the next steps. You can ignore the rest of the text that is shown for the purposes of this exercise.
To change how long your iPhone rings, dial
61*+1XXXXXXXXXX*11tt# where +1XXXXXXXXXX is the number you wrote down from the first step above and tt is the length of time in seconds for which you want your iPhone
to ring. To get the + sign to show up, hold down the 0 key for a couple of seconds and release it when it turns into the + sign in the readout above. Then press Call.
You may be able to go longer than 30 seconds - I have not tested it to see if it even works, but it may cause some of your plan minutes to be used even if you don’t answer the phone, so beware.
To give you an example, I dialed
61*+12537094017*1130# then pressed Call to change my iPhone ring to last 30 seconds. After this, assuming you’ve entered everything correctly, you’ll see the following message:
Setting Activation Succeeded
Voice Call Forwarding
When Unanswered