Yes desktop computers can connect to wifi internet.
If your desktop doesn't have built in wifi which most new ones today have you can get a wifi adapter antenna for your desktop computer that plugs into your usb port.
But if you go with a new desktop they will most likely have a built in wifi antenna to pickup wireless signals.
I like having wired internet on my desktop though as it runs faster. But wifi on a desktop is okay if you don't need really fast internet.