Hans de Vries (who happens to be a no-longer-active physics.SE user) has an online book (referenced below) in which ch. 6 is a presentation of an object he calls the Chern-Simons current, electromagnetic spin density, or Chern-Simons electromagnetic spin:
$ C^a = \frac{\epsilon_0}{2} \epsilon^{abcd} A_b F_{cd} = \epsilon_0 \epsilon^{abcd} A_b \partial_c A_d $ .
He has a long and detailed presentation of this thing, including graphs and examples. Unfortunately I'm not having much luck extracting from this what he claims is the interpretation of it, whether his interpretation is standard, and whether it has a classical interpretation. He references Mandel and Wolf (which I don't have access to), but what they apparently present is a different expression, $\epsilon_0 \textbf{E}\times\textbf{A}$, and refer to it as the intrinsic angular momentum of the electromagnetic field. De Vries says that $C^a$ is the natural way of making this tensorial. It seems hard to check whether what he's saying is standard, since he says, "The derivations (which I had to do myself since somehow one can't find these anywhere) and many details can be found in my paper..." (linking to a paper that duplicates the material in the book).
The expression is manifestly classical, so I don't really see how it's to be interpreted as the intrinsic or spin contribution to the field's angular momentum. The classical/quantum interpretation is also obscured because factors of $\hbar$ start appearing at de Vries' eq. 6.6, but these equations are supposed to be justified somewhere later on.
It seems odd to me that this is written as a product of the four-potential and a derivative of the four-potential. This makes it not manifestly gauge-invariant. If I was going to write down a density of angular momentum for the electromagnetic field, I would start from the stress-energy tensor, which is a product of $F$ with $F$, and therefore independent of gauge.
It's not at all obvious to me what one would even mean by a spin density for the electromagnetic field. I guess for a classical fluid of electromagnetic radiation in equilibrium (e.g., the kind of environment we had during the early universe), I would define a comoving frame and look at the amount of angular momentum $L^{ab}=r^ap^b$ in a small volume element. But that clearly isn't going to work for the electromagnetic field in general, since you can't define a comoving frame for, e.g., an electromagnetic plane wave.
It does make sense that the expression is manifestly translation-invariant, since if there is some sensible way to split the angular momentum into spin and orbital parts, only the orbital part should depend on one's choice of axis.
De Vries, Understanding Relativistic Quantum Field Theory, http://www.physics-quest.org/ , ch. 6