You can configure many call-handling features on the iPhone, but not the number of times an incoming call rings before it goes to voicemail. Only your carrier can change that variable. Wireless service providers uniformly grant incoming calls four rings within roughly 20 seconds before sending them to voicemail. If you find that ring length too short or too long, contact your carrier to adjust it. Otherwise, you can only force silent or nearly ring-less calls to voicemail by other means.
Some Rings Before Voicemail
Tap "Phone" on the Home screen, then touch "Keypad."
Dial "611," followed by "Call" to connect to your wireless service provider's customer support. Alternatively, dial the customer service number listed on the carrier or Apple's website (see link in Resources). Follow the prompts to speak to a live representative.
Ask the representative to increase or decrease the number of rings before an incoming call goes to voicemail. Different providers offer different options. Choose the one that best serves your needs and your carrier will re-configure your service accordingly.
No Rings With Airplane Mode
Swipe up from the bottom edge of your iPhone screen. Your Control Center displays.
Tap the "Airplane" icon to activate Airplane Mode and display an Airplane icon in the upper-right corner of your screen. This setting sends all incoming calls instantaneously to voicemail, without any rings to alert you.
Swipe up to get to your Control Center again and tap the "Airplane" icon to disable Airplane Mode. Then, tap "Phone," followed by "Voicemail" to listen to your voicemail messages and resume regular phone service.
No Rings With Do Not Disturb
Tap "Settings," followed by "Do Not Disturb." Toggle the Manual switch to the "On" position. A Moon icon appears on the upper-right corner of your screen.
Choose "Always" in the Silence section to hush all incoming calls while sending them directly to voicemail. Configure the settings on this page to allow only select calls to ring through, such as calls from your favorite contacts or at certain times of the day.
Tap "Phone" on your Home screen, followed by "Voicemail" to listen to your phone messages. Swipe up from the bottom edge of your iPhone screen and tap the "Moon" icon in your Control Center to deactivate the Do Not Disturb feature at any time.
You can also manually interrupt an incoming call’s standard number of rings and send it directly to voicemail. Tap the “Decline” button on the touch screen, press the Sleep/Wake button twice in quick succession, or squeeze and hold your EarPods’ center button for two seconds.
Toggle the Ring/Silent side switch of your iPhone to manually impose total device silence, not just from phone calls.
Not all carriers can reconfigure the number of rings before a call goes to voicemail.
Information in this article applies to iPhones running iOS 7.1. It may vary slightly or significantly with other versions or providers.