Something like
cd /var/ftp (or wherever you keep the files)
/usr/bin/find ./ -type f -mtime +7 -exec rm -f '{}' +
-type f file
-mtime + 7 older than 7 days
-exec rm -f '{}' +
That + at the end was something I found while googling--I'm trying to remember its purpose. Ah, I think it was a way to avoid getting the error of filelist too long.
http://www.hccfl.edu/pollock/Unix/FindCmd.htm
WARNING: DANGER and all that stuff.
I would definitely test it with echo rm rather than just rm before putting it into action.