Is there a symbol for the word "as"?

There is none. Should you choose to pioneer the use of such a symbol, might I suggest ~, since it's not good for much else. Looks like a worm in running away from something.

There are several shorthand systems that encode as in the form of symbols. The Pitman system uses a small circle above the line. It looks something like this:

  o
_____

A:B :: B:C = A is to B as B is to C

Thus :: = "as"