Territorial Representation in the Senate Act This bill allows each U.S. territory (American Samoa, the Northern Mariana Islands, Guam, Puerto Rico, and the Virgin Islands) with local legislative approval to be represented in Congress by a nonvoting delegate to the Senate who shall be elected by the people qualified to vote for officials of the territory. Further, the bill establishes qualifications for the office of delegate, authorizes the government of the territory to determine the election procedure, and provides that each delegate shall receive the same compensation, privileges, and immunities as any other member of the Senate.