Election Integrity Act of 2017 This bill amends the Help America Vote Act of 2002 to prohibit a state or local election official from providing a ballot for a federal election to an individual who desires to vote in person unless the individual presents a valid photo identification. If an individual does not present a valid photo identification, the individual shall be permitted to cast a provisional ballot. An election official may not determine that such an individual is eligible under state law to vote in the election unless, not later than 10 days after casting the provisional ballot, the individual presents: (1) the identification required, or (2) an affidavit attesting that the individual does not possess the identification because the individual has a religious objection to being photographed. With an exception for overseas military voters, an election official may not accept a ballot for a federal election provided by an individual who votes other than in person unless the individual submits with the ballot a copy of a valid photo identification. If an individual presents an election official with an affidavit attesting that the individual is unable to afford to obtain a valid photo identification, the official shall provide the individual with a valid photo identification without charge.