According to How to install ClockworkMOD Recovery on Sony Xperia Neo V this should be possible using UnlockRoot (download)1, which requires a Windows (XP/VISTA/7) computer. The process is described at How To Root Android Devices Using Unlock Root Tool, basically as follows:
- You should have a backup of your data (for safety reasons)
- Your device should be fully charged
- USB drivers for the device should be installed on PC
- USB Debugging must be turned on in the device
- Connect the device to PC using USB cable
- Run the downloaded tool, and Click on xe2x80x9cUnlock Rootxe2x80x9d, Thatxe2x80x99s it.
Another guide available is Learn How To Root the Sony Ericsson Xperia Neo V xe2x80x93 in case you are not satisfied with the described method ;)
1: The site hosting the tool unfortunately went down. With some luck, one of the results of this Google search has it.