If you look to the US Constitution for a simple yes or no you won't find any such right specified.
The framers of our Constitution and Bill of Rights were the well-to-do of their time and society at that time was almost exclusively dominated by white males. In many cases women were not even permitted to own or inherit property. The idea of voting was restricted to their own elite class but it was left to the original states to define who should be permitted to vote. Naturally, the "standard" thinking of the time was that only white, male land owners should possess that right. Their original concept of "Freedom" did not extend to their wives or children or to poor or merely average citizens.
Despite the rally call "No taxation without representation" used to generate enthusiasm for the revolution, there is nothing to require that you have any representation in our government as a precondition for being taxed. This would not, of course, impact negatively on the well-to-do class, who could count on having a vote.
On the one hand the US Constitution does not explicitly grant citizens a right to vote; on the other, several subsequent amendments specified below seem to do just that.
Freed slaves (but only black males) were specifically given the right to vote in federal elections by the 15th amendment. Women were granted that right by the 19th Amendment and persons over the age of 18 were given the right by the 26th Amendment. If you are a citizen and over the age of 18 it would seem that states are prohibited from denying your right to vote; thus even the 15th and 19th Amendments are rather superfluous in practice after that last Amendment. States could permit younger persons to vote if they choose.
The Voting Rights Act of 1965 adds added enforcement to protect the voting rights of minorities.
The 14th Amendment declares: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
The 17th Amendment of the Constitution requires that Representatives be chosen and Senators be elected by "the People". Can anyone be elected to office as required by the Constitution if "the People" don't have a right to cast their votes?
Exactly who are "the People"? Are they all citizens or just a select few based on some standard of wealth, status, and gender, as it was in the early years?
In each of the above amendments the people have been defined. Any citizen over the age of 18 regardless of gender, race, religion, or national origin. That is pretty much anyone other than a percentage who have forfeited that right, having been convicted of a crime in certain states.
Enter state voter-ID laws, almost exclusively written and passed by the right in a thinly disguised way to limit voting by the lower middle-class, poor, and minorities. The alleged purpose is to prevent voter fraud at the polls, an excuse totally unjustified by any facts.
Voter fraud does exist but it is vary very rare and has never been known to affect the outcome of any election in the United States.
Of 197 million votes cast between 2002 and 2005, only 40 voters were indicted for voter fraud, amounting to only .00000013 percent of the votes. In ten+ years Texas has convicted a total of 51 people of voter fraud but of those only 4 were for voter impersonation... the only kind of fraud an ID would prevent. Four in ten years is not a threat to democracy or election integrity, particularly when the "solution" would be to deny the legitimate vote to millions.
Talk about throwing the baby out with the bath water.
The National Voter Registration Act (42USC -- Chap 20) requires states to use a uniform voter-registration form for federal elections. The Election Assistance Commission (EAC) requires only that an applicant aver, under penalty of perjury, that he is a citizen.
The stated intention of the legislation was to encourage greater access to voter registration for the citizens who needed further assistance registering to vote. I am not aware of any voter-ID law that includes any added assistance to register.