How to prevent iPhone from vibrating during calls?
I believe you need to look in Settings > Sounds &amp; Haptics. 

In there you have various settings for Sound and Vibrate. Under the section "Sounds and Vibration Patterns" there's a "Text Tone" option. If you touch that, you have options for what happens when you receive a Text, both Sound and Haptics. One of the options for Haptics is "None"