You can use Engintron in order to run/install Nginx on your cPanel/WHM server.
Engintron is fully compatible with CentOS version 5, 6 and 7 on both 32-bit and 64-bit platforms. Additionally, users have already reported a 100% compatibility with CloudLinux versions 6 & 7.
Engintron is also compatible with both EasyApache 3 and EasyApache 4 as of version 1.7.0.
Installation is a process that lasts only a few minutes. You’ll need root SSH access to your cPanel server. Also check the current requirements (listed lower). If everything is ok, log in as root and type the following commands, one at a time:
wget --no-check-certificate https://raw.githubusercontent.com/engintron/engintron/master/engintron.sh; bash engintron.sh install
You can also check Engintron official install guide:
Hope that this helps!