Multi Mente can do it. But be careful when there are more than 255 directories. Then it bugs out, if I remember correctly. There are probably also separate tools, any MSX-DOS2 tool to do it will do it for you.
Improve can also sort the directory. However it, Multi Mente and DSORT only support FAT12 partitions. To sort FAT16 partitions, the fatsort tool that DarkSchneider recommended is a good choice for Linux and macOS systems. Meits reported in this thread that he used a Windows tool called Fatsorter.
Personally I don’t really use these tools, however I do use the sort function in Multi Mente quite often. On a FAT16 partitiion you can’t write it back to disk but I think it’s quick enough that I don’t need to.
