I was reading this article: http://plato.stanford.edu/entries/aesthetic-judgment/#1.4
I was thinking that aesthetic judgments are responses that derive from our emotions. So they can be considered rational after further inspection of how we react to the aesthetics of something and understanding why we reacted that way, but the initial stage seems like it isn't rational.
I'm not 100% on how to answer this question and would like some of you to weigh in and enlighten me.
Taking Kant's Critique of Judgement, there is a neat table at the end of the introduction (Ak. 5:198).
The faculty of judgement is one faculty of knowledge there, as different from reason and mind [Verstand]. In this sense, it is not rational, but purposive (its principle a priori), as rationality is often bound to laws and ends which are ascribed to mind and reason.
Another point is that in the first column it is stated that the mind is the faculty of knowledge for all faculties of knowledge. So every knowledge about/from judgement has to be rational. But this is not going very deep, because the interference of mind, judgement and reason is hard to understand. This in some sense has to be seen in the light of the Humean analysis, taking the deep difference between reflective and determining judgements:
Reflective judgement has to follow the maxim of purposiveness as it can only be purely inductive and in this sense is not rational (like causation is not rational in a strict sense). But determining judgement subsumes concretes under concepts by the very rules/laws of that concept (instated by reflective judgement) and is in a full sense rational.
"[So] the judgement of taste", as stated in § 1, "is not a judgement of knowledge, therefore not logical, but aesthetic" (own translation). Given that distinction it is quite clear that aesthetic judgements are not rational in a Kantian sense, but purposive.
As others have noted, the question you are asking is most famously addressed in philosophy by Kant's Critique of Judgment. Unfortunately, Kant's system is somewhat idiolectic and not amenable to brief, clear summaries. Phillip Klocking's answer, while accurate, has not only indicated as much, but--if I may be excused for saying so--demonstrated it as well.
Aesthetics refers in the Greek to sensation and feeling, and was often contrasted unfavorably with "reasoning" or logic. Its status shifted when the British Empiricists argued that all true knowledge was derived from the senses and only manipulated by logic, as if by a calculator. This left the validity of reasoned judgments and moral judgments open to skepticism. Weren't they just based in the senses, and thus purely contingent?
Kant was especially concerned about the "relativity" of morals. He attempts to show that our "judgments" are not randomly based in passing sensations. Our sensations and experiences are only comprehensible because they already have a rational structure a priori. This structure is not arbitrary, because it is necessary for all "rational beings" and "rational judgments." This inner structure of concepts organizes all of our sensations and judgments in an essentially "universal" way...at least as far as human beings go.
As you can guess, this places "aesthetics" in a different light. Prior to Kant, artistic judgments were considered a matter of "taste" and possibly "breeding." It was no more important to philosophy or reason than which food one prefers. No one would logically argue about which food is "better" or "truer." It's just a contingent matter of taste based on passing sensations and personal experience.
But Kant noted that we do indeed tend to argue that a painting, novel, or symphony is "superior" to pulp. That a beautiful old forest is "better" than a functional parking lot. (Kant was, in fact, more concerned with beauty in nature than art, and it is easier to see his arguments in this way. Not unlike E. O. Wilson's "biophilia.") When we make such aesthetic judgments, we do expect others to agree, as if to an argument. They seem deeper and closer to our innate "reasoning" than simple matters of taste.
Kant developed the idea of aesthetic judgment as a sort of pure "conceptualizing," in the loose sense, without content, a feeling of "purposefulness" minus any specified "purpose." It was not simply the casual impact of the senses determining a subjective judgment. It was an act of "inner causation," the pure exercise of our very powers of judgment.
Needless to say, all the gory Kantian details are missing in my crude synopsis. But I hope this gives you some direction. Kant was the first to reintroduce aesthetics into modern philosophy, and his Critique of Judgment is where your answer begins. In more recent philosophy, "linguistic structure" or "sociobiology" or "cognitive sciences" may pursue something similar, if less coherent, in their attempts to relate sensations to universal attributes of "mind," or rational judgment.
I think the quick answer is usually. Why so?
Aesthetics is a deeply intuitive experience at first. When one is stricken by a moral precept such as a taboo against rape or incest, it is easy to argue that morality might best be described by emotivism. And yet, if you've ever heard a theologian contort logic, angels on the head of pin is a short-hand for this phenomenon, clearly one's preferences can be buttressed by argumentation. Thus, one contemporary view coming from a naturalized epistemology on about axiological concerns (aesthetics, ethics, normativity, etc.) is that our primary preferences about anything may be rooted in our emotions and intuitions, but our language use is often rational. This is true of one's political philosophy which science suggests are correlated to biology, for instance. In fact, one hypothesis that is accumulating evidence among cognitive scientists is the somatic marker hypothesis.
Thus, aesthetic may be primary in the notion of a child being struck with awe and wonder at a piece of art, or it may be highly normative in the critique of a world's leading critic of painting. When a child exercises judgement, it will be intuitive, and when a critic does, highly rational. Thus, the question is not aesthetic judgement rational, but rather, to what extent.
It's worth considering that rationality itself is an aesthetic judgement. Rationality isn't 'right' so much as it's 'preferred' in certain activities and interactions.
Emotions are primary. Without emotions we have no motivation to do anything, and all rationality can do is provide us with an ambivalent roadmap of possibilities: an inner 'to be or not to be' debate with no real substance for making a choice. Rationality serves to channel, regulate, moderate, and otherwise focus our emotional impulses into fine-tuned action. Aesthetics is a goal that we we try to achieve, and rationality is a tool for achieving that end. Aesthetics doesn't come directly from emotions; aesthetics is coarse emotional impulses filtered and refined by the rational mind.
