Tribal Tourism Sovereignty Act This bill allows covered passenger vessels (e.g., foreign-flagged cruise ships) to comply with the foreign-stop requirement by calling on ports or places owned by an Indian tribe. Under current law, these vessels may not transport passengers from one U.S. port to another without stopping in a foreign country. The bill allows a voyage transporting passengers to call on a port owned by an Indian tribe if the voyage (1) is made by a covered passenger vessel that complies with security and safety requirements and certain training for crew members, and (2) employs alien crew members with valid nonimmigrant work visas. A vessel performing such a voyage must receive permission from the tribe to dock at a port or place owned by the tribe and disembark passengers on tribal lands. In addition, the bill outlines tribal powers and privileges, including that the tribe shall have the authority to levy and collect fees from port calls.