Can I use SPACE as mapleader in VIM?

Try the following instead:

let mapleader=" "

And remember to write the following line before that, to make sure spacebar doesn't have any mapping beforehand:

nnoremap <SPACE> <Nop>

Mapleader is a Vim string variable. To use space as leader, you must escape the special character.

let mapleader="\<Space>"

For more info see,

http://vimdoc.sourceforge.net/htmldoc/eval.html#expr-quote

EDIT:

This no longer works for me in my version of Vim. Even with the suggestion in the comments of unmapping the spacebar in normal mode by running nnoremap <SPACE> <Nop>.

I ending up going with the solution given in the answer below.

map <Space> <Leader>

nnoremap <space> <Nop>
nnoremap <nowait> <space> /