Note: Make sure your phone is Xiaomi's developer version, or it's gonna be extremely difficult to root.
Step 1: Unlock Xiaomi. Xiaomi's policy sometimes requires you contact Xiaomi representatives online. Make sure you have done that.
Step 2. Download TWRP and SuperSU 2.76
Step 3. Once get everything ready, flash in TWRP on computer with the ADB command (check TWRP for exact code)
Step 4: Enter TWRP and flash in SuperSU!
So yes! Xiaomi Redmi Note 4 CAN ROOT!