USB OTG ("On The Go") support has been part of the Android OS since about version 3.1, however that does not imply that all phones running Android 3.1 or higher will work with an OTG storage device. Each phone manufacturer and each model for each carrier has changes to the base OS and may not have all the settings and drivers needed for OTG functionality.
You should confirm with your cell phone carrier or alternatively, there are a number of OTG "checkers" available on the Google Play Store. Search the Google Play Store for "OTG checker" and you'll see quite a few. We haven't tested any of them and we're not recommending any of them. It is just an option that you can choose.