What is a duty? We may well consult the dictionary: a good working definition is one of those, indeed the most relevant one to this discussion, given by Merriam-Webster: a moral or legal obligation.
What, then, is a civic duty? Clearly, a civic duty is a moral or legal obligation to one's community. However, it is clear from the innate concept that a civic duty is determined on the community level; that is, at the very least, the way it is used commonly. In order to maintain this usage, can we nail down a definition based on the previous discussion? What we seek must be the established duty of a person towards his or her community, based upon either moral grounds or legal grounds. The case of legal grounds is trivial and requires no further discussion, as I'm sure you'll agree; let us consider the more nuanced case of moral grounds.
One might think that communal morals might be the morals held in common by each member of the society. However, it is utterly unreasonable to expect that an entire large population would have enough in common to establish such a common code. We may consider, however, an overarching set of morals for a society that represents not something that each individual holds personally, but rather something that each individual accepts as the communal idea. Indeed, this is the nature of law; not every person wishes to comply with every law, but many comply despite disagreement because the law is what is established. The existence of this "umbrella" moral code is necessary for a "civic duty" to have any meaning if not established by legislation.
Can we therefore find this elusive community moral code and characterize it? It may indeed be very difficult, and we have not even proven its existence. For brevity, let us assume it does exist. Being part of the society in which the community code is accepted, we may at least be able to flush out some of its qualities. As we have observed, it must be the sort of non-obligatory moral analog of law, something with which perhaps we do not agree but nevertheless that we recognize as conduct to be expected. We can identify characteristics of this code: politeness, industry, honesty, and altruism, to name a few. Just as not all observe the law, not all observe these. Thus, a civic duty, when not legally mandated, must be mandated by the common moral code. We have as such completed a satisfactory characterization of civic duty.
Now, in answering the question "Is voting a civic duty?" we may be inclined to respond immediately to the affirmative, as this presumed principle seems to be the predominantly accepted norm as presented in our common education. Does the rhetoric agree with reason? One need not think too hard on this question to come to an answer: by our definition above, voting is a civic duty as long as it fulfills some common social moral expectation. This is a necessary condition to be fulfilled because voting is not legally compulsory.
What social mandate is fulfilled by voting? Let us consider this. The results of a vote are that either one decision is made or another. Any outcome has some inherent value to the benefit or detriment of society. If any outcome has equal value, then a vote for one option delivers no value that would not be delivered by a vote for another, and the vote certainly has no net effect on society and therefore cannot be expected to fulfill any social expectation. We must, then, assume that different options have different net values. One option, in short, is "better" than another.
But how are these values determined? Is there an extrinsic value, or is the value dependent upon the people involved? In other words, is there an absolute right or just the relative right to the desires of individuals? We need not concern ourselves with divining the solution to the philosophical problem or moral relativism. Let us consider both possibilities.
If there is an absolute right choice in a vote, then indeed to vote for that choice would deliver to the rest of society a net increase in value; this would be the social expectation. However, the question then becomes that of determining the absolute right. Experience has shown that decisions are often made by narrow margins in a vote, demonstrating the inability of at least nearly half of society to determine the right. If we cannot reasonably determine the right, can we be expected to deliver the value desired? This we may simply leave as an open conclusion: if there is an absolute right answer, voting is a civic duty only with the assumption that the voter is willing and able to distinguish the right from the wrong and choose correctly.
On the other hand, if there is no absolute right, then values are relative to the observer. I may see one decision as a significant benefit, whereas you may see the same as a detriment. Indeed, superficially this appears to be the current state of affairs. How does one deliver to society the value expected by communal moral code given this observation? Obviously, one must choose the option that delivers the greatest amount of communal value; however, this undermines the establishment of voting as a means of determining the true opinions of the population, for everyone in line with his or her "civic duty" will vote on a certain decision regardless of personal belief or opinion. We arrive, thus, at a paradox: if voting is a civic duty, then it fails to accomplish its own purpose. On these grounds we must conclude that voting is not a civic duty.
We have covered much ground and leaped over more chasms than perhaps we ought to have done, but the reasoning is rather clear: it appears that voting is very likely not a civic duty in that a single voter may very well do nothing to fulfill overall social expectations in voting. On the other hand, if voting is a civic duty, then so too is a diligent effort to find the "right" decision for the community, and only with this diligent effort is the duty properly done.
Either way, this does not mean that one must not vote. Rather, it means that one's decision to vote more likely ought to be determined personally, according to personal moral code and desires, and not by others who would argue that it is the "right thing to do" for the community.