I have a printer that I bought which is wireless only to find out that my computer doesn't have wi-fi capabilities. Can I hook it up anyway or do I need to get a wi-fi card?

If the printer only has wireless connectivity, some type of wireless device will be needed to connect to it. Some possibilities are a wireless adapter card in the computer, a wireless USB adapter, or connecting the computer wired to a wireless router. What is the printer brand and model?

First, it would help if you listed the printer make and model. But I've never seen a printer that doesn't also have a USB connection as well as a wireless one.

Another point, is that, your computer doesn't have to have a WiFi adapter to print to a wireless printer. If you do have a wireless network, and install the printer on the network, then any computer on the network can print to it. If you don't have a network, then you are probably going to put the printer next to the PC so just connect using a USB cable.