National Intersection and Interchange Safety Construction Program Act of 2017 This bill directs the Department of Transportation (DOT) to establish a national intersection and interchange safety construction grant program. DOT may make competitive grants to a state or local government, U.S. territory, tribal government, or metropolitan planning organization for projects that: are eligible for federal-aid highway funding, and will improve the safety of intersections or interchanges on the National Highway System that are used by an average of 50,000 vehicles a day and that are in immediate need of safety improvement. The aggregate grant amount provided to an entity in a fiscal year shall not exceed 5% of the amount available for all grants under the program in that fiscal year.