In particular, it means it can't find the static version of the C library, because you are compiling with -static. This means that it can't use the standard shared library, typically something like /lib/libc.so.
In order to support building static binaries, you would need to install the appropriate static library (libc.a), which may or may not be available in pre-packaged format for your distribution. Under Fedora, this is available as the glibc-static package:
yum install glibc-static
With this package installed, I can build a static binary from your sample code without a problem:
$ gcc -static -o exit exit.c
$ file exit
exit: ELF 64-bit LSB executable, x86-64, version 1 (GNU/Linux),
statically linked, for GNU/Linux 2.6.32,
BuildID[sha1]=12c642ecc01622c623c2efa5efa7e23d73889808, not stripped
Other solutions include building the static C library yourself, or working with a smaller C library designed for embedding, such as uclibc or musl. These are smaller and typically more amendable to static linking. This would may also involve building the library yourself.