Let America Vote Act This bill requires states to allow unaffiliated voters to vote in primary elections for federal office. It also restricts certain federal election funding for states that allow noncitizens to vote in state or local elections. Specifically, each state must permit an unaffiliated voter who is registered to vote in a federal election held in the state to vote in any primary election for federal office. A state shall not permit an unaffiliated voter to vote in primary elections for more than one political party. The bill prohibits a state from (1) sharing unaffiliated voter information with a political party or any other person who may reasonably be expected to use the information for political purposes, including soliciting funds; or (2) treating an unaffiliated voter as a member of a political party for purposes of the state's official voter registration list. States must, in order to use federal election administration funds, certify their compliance with these unaffiliated voter requirements. Upon certification, the Election Assistance Commission (EAC) must make five-year grants to the state for the costs of permitting unaffiliated voters to vote in primary elections. The bill specifically prohibits noncitizens from voting in federal elections. (Current federal law prohibits noncitizens from voting in federal elections.) A state may not use federal election administration funds unless the state certifies to the EAC that it does not permit a noncitizen to vote in state or local elections or vote on any ballot initiative or referendum held in the state.