On 2 June 1924, a small piece of legislation was enacted that gave "blanket" US citizenship to Indians.
Of course, at the time, a great many had already "earned" citizenship by proving their "competency" as part of the General Allotment Act ( Dawes Act, 1887 and 1891 amendment) and subsequent Burke Act (1906). For conforming to these Acts (part of which was showing that they had become "civilized") was that after a period of 25 years, full ownership of the allotted land—which had been held in "trust" (land which had belonged to the tribes as a community and had been parceled up for individuals/families by the government)—would be given to the respective Indian(s) as well as a grant of citizenship. (The Burke Act eliminated the 25 year trust period, making the amount of time a discretion of the Secretary of the Interior.)
As the General Allotment Act was a means for promoting the policy of "assimilation" of the Indians from their "savage" or "primitive" culture/society—also a means to take care of the "Indian problem" and open up what became millions of acres to settlement and use by others—to the (white) civilization (and all its attendant culture and values, including religon), so was the Indian Citizenship Act. The Indian was to become an American, not remain an Indian and a big part of that, it was felt, would be bestowing citizenship.
Certain provisions for citizenship had already been made for Indians who were World War I veterans (a bit late in coming considering many were conscripted) and the 1924 Act was meant to cover any remaining Indians (estimated at around 125,000). Though the General Allotment Act allowed gaining citizenship, it did not provide for voting rights:
And every Indian born within the territorial limits of the United States to whom allotments shall have been made under the provisions of this act, or under any law or treaty, and every Indian born within the territorial limits of the United States who has voluntarily taken up, within said limits, his residence separate and apart from any tribe of Indians therein, and has adopted the habits of civilized life, is hereby declared to be a citizen of the United States, and is entitled to all the rights, privileges, and immunities of such citizens....
(though one wonders why voting rights would not be included in "all the rights, privileges, and immunities" of a declared citizen of the United States). As can be seen by the text of the Citizenship Act, it also doesn't clearly state voting rights, but as a consequence, most states did give the right to the "new citizens"—though because of the wording, a few states withheld that right (New Mexico, Arizona, and Maine until after World War II). Later amendments clarified that the Act extends to Alaskan Natives.
(Sources: Carl Waldman Atlas of the North American Indian, rev. ed., 2000, General Allotment Act quote from www.csusm.edu/nadp/a1887.htm, text of Indian Citizenship Act from http://members.stratos.net/cpetras/ci-4-4.htm)
{Cite as 43 U.S. Stats. At Large, Ch. 233, p. 253 (1924)}
CHAP. 233.—An Act To authorize the Secretary of the Interior to issue certificates of citizenship to Indians.
Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, That all non-citizen Indians born within the territorial limits of the United States be, and they are hereby, declared to be citizens of the United States: Provided, That the granting of such citizenship shall not in any manner impair or otherwise affect the right of any Indian to tribal or other property.
Approved, June 2, 1924. June 2, 1924. [H. R. 6355.] [Public, No. 175.]
SIXTY-EIGHTH CONGRESS. Sess. I. CHS. 233. 1924.
See House Report No. 222, Certificates of Citizenship to Indians, 68th Congress,
1st Session, Feb. 22, 1924.
Note: This statute has been codified in the United States Code at Title 8,
Sec. 1401(a)(2).