Well, technically yes. The only Constitutional guarantees for voting rights are those laid out in the Fifteenth, Nineteenth, Twenty-Fourth, and Twenty-Sixth Amendments, which state that voting rights cannot be denied based on race, color, former slavery, sex, failure to pay taxes, or age past eighteen. Note that religious freedom is actually not listed; the Constitution states that religious tests are prohibited as qualifications for "any Office or Public trust under the United States", but that refers only to being a candidate, not a voter. States can lawfully impose any limits they want on voting rights other than the above, although there have been successful Constitutional challenges on the basis of the Equal Protection Clause.
But if we're going for technicalities, it would actually be perfectly Constitutional for a state to create its own nobility and to limit voting to members of that class, or even to a foreign country's nobility! The Constitution only prohibits the federal government from granting titles of nobility, and only federal office holders are prohibited from holding foreign titles of nobility.