You can follow the tutorial to root your phone by yourself.
As Asus’s first attempt at a mainstream budget phone, Zenfone 4 has a colorful design, a decent internal storage and a feature-packed camera app. If you have purchased it and want to get it rooted, you can follow the following steps.
Step 1. Backup all important data and files in your device to prevent data loss.
Step 2. Download USB driver for your device and install it in PC.
Step 3. Open USB debugging mode and power off your device. Then hold Volume Down, Volume Up and Power button simultaneously to enter DROIDBOOT mode.
Step 4. Connect the device to PC and you’ll see “Ready for Download” on the screen of your phone.
Step 5. Download Root_Zenfone 4_T001.rar and extract it to a folder in PC.
Step 6. Open the folder, press “Shift” button and right click at empty space, you’ll see “Open Command Window here” option. Click it to open a command prompt.
Step 7. Type “fastboot erase cache” and hit “Enter” key. Then type “fastboot flash update root_zenfone4_v4.2.0.zip” and press “Enter” key again.
Step 8. After the process finished, check if you can find SuperSU app in your device. If yes, it proves that you are rooted successfully!
Also you can try Super Root Android which provides simplest and safest rooting ways. It can root many Android devices by only one click! Unrooting function is also provided its the interface.