Closer to the total solution
So, I attempted to install 'Clam AV' from the 'Software Manager' and it seemed like it downloaded it. However, when I looked in my 'LM Menu' it wasn't found. Linux Mint likes to put it's 'System Tools' into 'Administration', but even a look here yielded nothing.
The solution that jfblaze gave worked like a charm, but I wanted the GUI solution that has been used on Ubuntu. Luckily, I had an Ubuntu machine running with ClamAV on it and looked at what it was calling up.
Try this from your terminal window:
sudo apt-get install clamtk
Then in your GUI (without the quotes):
right click -> Create Launcher -> Type: "Application" -> Name: "Virus Scanner" ->
Command: "clamtk %F" -> Comment: "Scan for viruses..."
It won't have a cool icon for it, but at least now you can run it.
It worked for me and I hope it will work for you too!