Yes... read about USB gadget interfaces. However, you need a particular type of hardware called a USB host card which aren't the same as "ordinary" USB ports - there are plenty of these about but they are not what you would call "normal" hardware.
For instance, things like the GP2X games console run Linux and can act as USB host (i.e. appear as a mass storage device) but that's because it's got one of these chips in it. Basically, USB devices are "clients" and most USB ports on computers are "servers". However what you want to do is for your computer to act as a USB "client", which requires USB "gadget" software and compatible hardware.