Yes, you can. Buying a wireless network adapter would be the easiest way to do so, yes. Be sure that the chipset your adapter uses has Linux drivers. If it doesn't, it can often be made to work, but it's easier to just plan ahead a little.
Some distros (best known is Ubuntu) have a list of tested wireless network cards and their success in installing them and getting them to work. I would check with your distro to make sure what you're getting will work. Not everything works with Linux, especially wifi cards.