When you install CyanogenMod now, it will seem as if you do not have root access. You actually do but CyanogenMod has turned that off. I was surprised and started trying to root my phone. Luckily, nothing bad happened but you do not need to do this!
Enable developer options by:
- Going to Settings
- Select About Phone
- Tap Build Phone multiple times
- Return to the Settings menu and select Developer Options
- Select Root Access and give your Apps and ADB root access!
You can try to install SuperSU but CyanogenMod has Privacy Guard to manage your SU requests.
That is a safe and fun way to root your phone running CyanogenMod safely.
Sources
Man and Keyboard 