That depends. Is your USB port recognized? Say, if you attach a mouse or keyboard to it--do those work? Or do you have a bigger problem, with your USB port not being recognized.
Before you buy something new, perhaps, if you haven't already, post on the hardware support section of the forum the make & model of your USB hard disk and ask for help on getting it to work?
If you want to buy something new, research it a bit for Linux compatibility (if you do an Internet search for the make and model of the device you intend to buy, and add the word "Ubuntu" or "Linux", and you find nothing but bug reports and problems from other users, perhaps skip it). You can also check the Community site, where there is a hardware database you can search: http://community.linuxmint.com/hardware/welcome
. Linux Mint users post their experience with their hardware devices and peripherals there.