Sony Xperia Z1 USB hosting demo
If so, it is possible with devices that support USB hosting or USB on the go (OTG).
The Xperia range of devices has done this for some time, the Xperia Z1 is another handset to continue this support.
With the appropriate cable (available here) you can connect USB memory sticks and more to your device. View the content, copy or even edit it.
Watch the following video to see it in action.