If you mean the general right to vote, that isn’t explicitly enshrined in the U.S. Constitution. The Constitution enumerates the right to vote for U.S. Representative and Senator provided one meets the qualifications for the most numerous branch of the state legislature (Art. I, sec. 2, 1789; Amend. XVII, 1913). State governments were explicitly prohibited from abridging the right to vote based on certain enumerated characteristics: race/color/prev. servitude (XIV, 1870) and sex (XIX, 1920). During and after the civil rights movement we added: failure to pay taxes (XIV, 1964) and age (XVI, 1971).
“I do not think the enjoyment of the elective franchise essential to citizenship”. Dred Scott v. Sandford, 60 U.S. 393, 581 (1857) (Curtis, B., dissenting).
“It is clear, therefore, we think, that the Constitution has not added the right of suffrage to the privileges and immunities of citizenship as they existed at the time it was adopted.” Minor v. Happersett, 88 U.S. 162, 171 (1874).
“Certainly, if the courts can consider any question settled, this is one. For nearly ninety years the people have acted upon the idea that the Constitution, when it conferred citizenship, did not necessarily confer the right of suffrage.” Id. at 177.
“The Fifteenth Amendment does not confer the right of suffrage upon anyone.” United States v. Reese, 92 U.S. 214, 217 (1876).
“The privilege to vote in any State is not given by the Federal Constitution, or by any of its amendments.” Pope v. Williams, 193 U.S. 621, 632 (1904).
This line of precedent ran right up to Breedlove and Lassiter in 1937 and 1959 respectively. Suffragettes had been pushing to abolish poll taxes since 1920, but the big payoff at a federal level came after joining hands with the broader civil rights movement in the '60s.
And this is just one part of the legal side of the civil rights movement. The legal foundations of civil rights in this country were torn down and rebuilt in very short order. For example the double jeopardy clause wasn’t held applicable to the states until 1969, overturning a thirty year old precedent. The right to an attorney at government expense wasn’t recognized until 1963, overturning a twenty year old precedent. In the space of two years, 1962-1964, the Court overturned a 16 year old precedent and ruled that electoral districts just about everywhere violated the equal protection clause, apparently a continuous violation since the amendment was passed ninety years prior. &etc, etc, etc.
~Max