Note, see the title? Please don't deploy webpages with FTP, use some sort of version control system and automate that with a build system, there are plenty of those!
So, my old computer screen broke and I needed some files from it. I couldn't see a thing, yet I knew how to open a terminal and type commands (another reason on why you should learn some scripting).
From my old computer, putting my files recursively:
scp -r ~/path/to/dir/* firstname.lastname@example.org:/home/u/user/folder/
From my new computer, getting my files recursively:
sftp email@example.com cd folder get -r *
There you go. It will get all those files from the current folder you are. Use !ls to see where that is.