Traditionally the file was called README in uppercase because command-line environments that use alphabetical ordering would then put the file at the top. This makes them easily visible in big directories.
It's most likely a holdover from the Unix/Linux world where you would download sources and then build your software. Having files like README and INSTALL at the top of your 'list directory contents' view makes it easier to see that they are there, instead of having to browse the entire contents from a command-line interface. The same basic principle works for github as well (and actually works in GUI interfaces too, come to think of it, so it might still hold merit)
By no way a hard rule, but very likely something that everybody is doing as a habit because other projects are doing it. Unless there is some explicit reason NOT to, you should probably use all caps just because you'll see it being used that way in lots of other projects. It's also the default naming Github uses when you create a new repository.