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The feature you are talking about is know as USB OTG. Not all Motorola phones have that feature but most of the models does have it. Motorola doesn't specially mention it for their phones. You can buy the USB OTG cable, then connect it to your phone and then connect the memory stick. If it recognized the memory stick, that means it is OTG capable. The OTG cables are very cheap. You can get it for less than $2. See here --> http://www.ebay.com/itm/USB-Micro-B-Male-to-A-Female-Adapter-Converter-OTG-Cable-for-Android-Cell-Phone-/321519674372?hash=item4adc10e404:g:UZYAAOSwPe1UEdyN
You can get it from most of all local mobile stores or electronics stores.
If OTG is not working, then you can get a Wireless USB drive. So you can transfer stuffs from your phone to the USB drive without OTG. See here --> http://www.amazon.com/SanDisk-Wireless-Smartphones-Tablets-SDWS2-032G-E57/dp/B00DBX371C
(These wireless USB drives are costly though)
You may also need to download a File Manager from Play Store to transfer contents to memory stick. You can download Astro File Manager. Astro will recognize the memory stick.
If you have any questions or would like any additional information, please don't hesitate to ask.
If this is not the information you are looking for, please don't rate me bad or poor. Instead please let me know and I will continue to help you.