I think what you mean is that you want a font. I believe the people who usually do that are now graphic artists, but you could also look for a calligrapher. Probably.
Do you mean creating a script (an encoding of the spoken language into symbols), or creating a set of glyphs (pictures that represent those symbols)? The latter is done by a font designer, while the former is normally done by a linguist.
Three Islands Press, at www.3ip.com, is an example of a company that designs and sells fonts. I’ve given some of their antique script looking fonts as gifts and also had a couple of completely fascinating and pleasant conversations there with a designer - the designer? - well, they seem like a fine little outfit.
I have no interest in their success, just passing on information.