There are ways to prevent your iPhone from making noise when you have an incoming call. Whether you do this with a hardware mute switch or software settings, the iPhone has several ways to turn off or customize the ringtone.
All iPhones: No ringing on incoming calls? Simple solution!
The easiest way to turn off the iPhone ringtone is to flip the hardware switch on the left side of your iPhone. This switch is located above the two volume buttons on most iPhone models. This is your iPhone’s physical mute switch.
To put your iPhone into silent mode, slide the switch down so that the orange indicator on the switch is visible. When you do this, a bell icon with a line through it will briefly appear on your phone's screen to confirm that your iPhone has been muted.
To wake up iPhone from silent mode, slide the switch up towards the front of iPhone and the ringer will turn on. Another icon will appear on the screen to indicate that the phone ringer is active again.