How to Root Android Phone Without Computer
First, you need to check your device compatibility from here Check Your device here first (Tx XDA forum)
Install Framaroot app from here Framaroot, a one-click app to root Android
Root Android Phone: you can also use KingRoot android app to root the android phone without a computer in one click
Download KingRoot from here Click Here
If your phone is unrooted, you can see the prompt saying that “Root access is unavailable“. Then click the button “START ROOT”
When rooting, you can view the progress. When it is completed, you will see the big green tick icon. After that, you can remove the king root app.
If you want to check your device is rooted or not then install root checker from here to see your device is successfully rooted or not.
For more, you can refer Xda forum for any detail about rooting any device.