OTG is a feature that is needed to be supported by the hardware of your phone. You cannot enable the feature just by rooting your device. Rooting gives you root permissions as far as software is concerned. USB OTG functionality is definitely a hardware based feature.
If you are sure your hardware supports the OTG function, then you may need to install a custom kernel to enable it. You can search for it over the XDA developers forum. Please note that most of the kernels and mods available on XDA are developed by software enthusiasts who are not necessarily experts in the arena. Also the mods developed may not have been tested on all devices. You need to be careful while dealing with them. Kernels are device and build specific. Of you install a wrong kernel, you may run the risk of bricking your phone. I would advice you not to indulge into it if you are not an expert in the field.
Chainfire seems to have an app for enabling the OTG service. Search for the app on Play Store. If the phone software is not providing the support for OTG, but hardware does - this could e your solution.
Some users have stated that ES File Explorer is a great tool for making use of OTG functionality even when it is not supported by your phone software. Connect any of your external drives to your phone and search for it on ES File Explorer. If the drive is recognized, it will be shown up as a separate folder. The app works even when you are not rooted.
Please note that enabling OTG on a phone that does not support is needs quite a good knowledge of software and hardware. Besides, it may or may not work. There would be the cases, wherein even if you enable the feature you may end to power the external drive using some external power, the phone may not power the drive.
Live....and Let Live!
