If the player is a bad RP'er, a bad sport, or a bad writer, that's enough reason there to reject them. A lot of RPs have a minimum writing standard. Don't let technicalities make you keep them. I've seen a dozen GM/player mistakes where they let a problem player stick around because they didn't think there was a formal rule broken, or couldn't reject them for similar reasons. Bad idea.

If this is your problem, the previous advice works. Tell them they don't fit the kind of writing style or skill you're looking for, and wish them luck, or work with them to improve the problem and teach 'em something. Give them constructive criticism on what they should fix. If they're good-natured and cooperative, then I'd push you to give 'em a shot until they prove you shouldn't. If they put up an attitude and won't work with you, then that's a huge red flag and a green light to kick 'em out. 

Don't get wrapped up in the writing flaws or pet peeves that bug you unless they're damaging. Not enough (particularly new) players get a chance when they're borderline acceptable, and they're usually not that bad and will rapidly improve.