For future googlers, I've found this plugin very useful. It has option to define character order for non-latin languages.
Older versions (jQuery dependent)
$('.submenu > li').tsort({
charOrder: 'abcçdefgğhıijklmnoöprsştuüvyz'
});
For English only characters, no option is needed to define
$('.submenu > li').tsort();
Current version (jQuery independent) (29 March 2016)
Current version of tinysort is now independent from jQuery. Pure JavaScript. I updated jsfiddle for new version usage.
tinysort('.submenu > li', {
charOrder: 'abcçdefgğhıijklmnoöprsştuüvyz'
});
Demo
http://jsfiddle.net/ergec/EkScy/
Website
http://tinysort.sjeiti.com/