Is there anything even close to a "standard symbol" to indicate that a diagram is required to commute? It is evident from contemporary mathematical practice that there does not exist any usual notation to denote that a diagram commutes. This is almost always stated in meta-language above or below a diagram. 
Questions. 
Is there anything even close to a standard symbolic notation to indicate that a diagram commutes? Maybe in higher category theory?
Is there any noteworthy book or paper which makes use of a symbol, regardless of whether this is to be considered standard or advisable,  instead of using surrounding words to impose the condition of commmutativity?
Remarks.


*

*Part of the motivation for this question is wishing not to have to make up a symbol if there is any noteworthy precedent in the literature, but, needless to say, I have never seen any such.

*Since there is e.g. a standard symbol to denote pullback diagrams, it seems somewhat surprising that the contemporary consensus seems to be to use surrounding words instead of a symbol.

*Of couse, the omission of certain composite morphisms in a diagram can be seen as some sort of signalling that a diagram is required to commute. The iconic example is a commutative square, in which, for good reason, the two composites are not drawn, and one could see this very omission to by indicative enough. Yet, to me, this seems not to yield a precise pictorial language, least of all when it comes to using diagrams as input to machine-computations. 

*I seem to recall to have once read a paper, which I do not find, saying that in the early days of category theory the writing style in books and papers was more diagrammatical than nowadays, so, it at all, a notational convention such as the one I am looking for might be found in early category theoretical papers.

 A: The closest thing you'll get to a "standard" symbol is to insert an identity 2-cell. $$\require{AMScd}
\begin{CD}
A @>f>> B \\
@VhV\qquad\!\!\Downarrow\, id V @VVkV \\
C @>g>> D 
\end{CD}$$
This necessarily requires the two ends are equal just like the identity arrow requires the source and target objects are equal. This can be generalized to any dimension. 
Usually diagrams are assumed to commute and no additional notation is necessary. Indeed, you occasionally see notation to explicitly indicate that a diagram doesn't commute.
A: To get this notational question wrapped up, here is a summarizing answer.
Generalities.
Needless to say, marking out diagrams as commutative is unusual,
and---if done badly--spoils them.
The beauty and usefulness of commutative diagrams lies in that they contains hardly anything unnecessary.
There can be reasons for a symbolic notation though, in particular if one in a proof works with multiple diagrams, as mathematical objects in their own right, and finds accompanying words lying about somewhere in their periphery inadequately precise.
This is why I, personally, opted not to use any symbol within the diagram, neither the $\circlearrowleft$ kindly suggested by Osama Ghani, nor the $'''$ suggested by Arnaud D., nor the rotated # kindly suggested by Hans Lundmark, in the comments to the OP, nor even the identity 2-cell kindly suggested by Derek Elkins in one of the answers (in the example below, one would need more than one higher cell, which brings about new problems, while the intent is just to mark the diagram in its entirety as commutative). 
In my work, I use rectangular light-gray frames around the diagram, annotated with the word "commutes", always at the bottom of the rectangle (see below). 
For certain purposes, it still seems to me that 
a standardized notation for a diagram being commutative
is useful.
Please note that the below is unusual; I'm just adding it here to suggest
to others one of the infinitely-many solutions one can find to this notational problem.
Your mileage may vary.
Examples.
Model-theoretically speaking, while

represents a quiver,

represents a set of axioms($=$ set of pairs of words over a signature of category theory).
In this convention, the frame around the diagram changes its type.
Caveat emptor, this notation is not attested in the literature, for all I know, there may be someting subtly wrong with it eluding me.
