How to turn a USB to a memory card for play station 2 (PS2)?

You can do this using a program called Open PS2 Loader, it will let you create virtual memory card images on a USB storage device. Unfortunately it doesn't seem to work with games loaded from disc. You have to boot the game from a USB drive, internal hard drive or network share.

Note that since it uses memory card images, not save games, it won't work directly with saves downloaded from the Internet. You'll need to move the save game to the virtual image before you can use it with the game, just like you would with a real memory card.