November 5, 1912
Despite some claims that Arizona was the first state to grant women’s suffrage, this is a mistake. The Arizona Constitution included women’s suffrage when it was ratified and Arizona became the 48th state admitted to the Union in 1912.

However, several other states had already granted women the same voting rights as men, including: Wyoming (1890), Colorado (1893), Washington (1889), Utah (1896), and California (1911). In some cases, women’s suffrage was gained when these were territories and before statehood. In other cases, women’s voting rights were secured after statehood.

This link seems to be authoritative: http://womenshistory.about.com/od/suffrageoverview/a/timeline_us.htm
This link gives the chronology of statehood: http://klishis.com/Misc/State.php
Note also that some states, notably Kentucky and Kansas, originally granted women only limited voting rights, such as in local school elections.