You can movie your iTunes Library to an external storage device, you cannot move the actual iTunes application however.
To move the library if its all located in one place and is consolidated, you can simply drag and drop the entire iTunes Folder in your profile's Music Folder to the SD card.
Once it is copied over, you can start the iTunes Application with the shift key held down and it will ask you to point it to the library to open. Just navigate to the iTunesLibrary.itl file in the SD card and select it. It should then open in iTunes and will work as it has.
If your iTunes Library is not consolidated, see here to make to portable first, and then move it to the SD card. Link-> Make a split library portable - Apple Community