They have no right to vote, but the Constitution very explicitly requires that they be counted for purposes of apportioning the House of Representatives:
Fourteenth Amendment, Section 2: " Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State..."
Section 2 of the 14th Amendment to the Constitution provides, “Representatives shall be apportioned among the several states according to their respective numbers, counting the whole number of persons in each state, excluding Indians not taxed.” Section 1 of the same Amendment provides, “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 order of these two Sections implies that the persons upon whom apportionment is to be made are persons born or naturalized in the United States.
No one in 1868 envisioned a mass invasion of foreign nationals, as can be found by simply reading Howard's many Senate comments. The intent was to give Black people rights under the Constitution that could not be nullified by State laws. First, they were to be made citizens, and second, they were to be guaranteed citizen's rights, nullifying Dred Scott. Of course, one of those rights is the right to equal representation - not 3/5ths. Thus the language of the 14th.