While you are in messages press the menu key on the bottom right of your phone (the 3 horizontal lines) and a window will pop up , select settings and then under notifications you will be able to select vibrate.

Since the ZTE Savvy uses Android 4.1 Jelly Bean, it should be possible to set it to Vibrate mode by pressing the Volume Down button until you feel the phone vibrate and a vibrate icon appears on the screen. Try to do this first and see if it takes care of your concern.