This
ToCharacterCode["123abc"]
returns
{49,50,51,97,98,99}
and
Fold[256*#1+#2&,0,ToCharacterCode["123abc"]]
returns
54091680146019
I got all that by wandering around the help pages with a few lucky guesses.
If the size of the numbers, within reason, do not really matter then perhaps that does what you need, as long as you don't include things like Greek characters and other special characters that have a character code greater than 255.
Or if you really need to compress the range of the result then perhaps you could write a simple Piecewise function that would be mapped onto the output of ToCharacterCode and would reduce the range of character codes down to something you like better.