Women's voting rights became available because of the Suffrage Movement which started in 1848.
The Movement ended in 1920 when the secretary of state proclaimed the 19th amendment had become a part of the constitution of the United States.
This Amendment states; "The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex. Congress shall have power to enforce this article by appropriate legislation."