When receiving a text or phone call, your iPhone’s default settings will cause it to vibrate. Though the vibrations aren’t particularly annoying, you can turn them off whenever you want. Or, if you want to customize your own vibrations, you can do so in the Settings option.
After opening up Settings, navigate to Sounds and then Sounds and Vibrations. Tap on the Vibration option and begin recording a new pattern. Every time you tap the middle of the screen, you’re inputting the next vibration sequence. You can do this for each of your contacts if you wish, though that could take ages.