Drone Integration and Zoning Act This bill requires the Federal Aviation Administration (FAA) to prescribe regulations or standards related to unmanned aircraft systems, commonly referred to as drones. The FAA must designate the area between 200 feet and 400 feet above ground level for use by (1) civil drones, and (2) commercial and recreational drones. The bill prohibits the FAA from authorizing the operation of civil drones within 200 feet above ground level above private property without the property owner's permission. For structures over 200 feet above ground level, the FAA may not authorize civil drone operations within 50 feet of the top of the structure or within 200 feet laterally, whichever is closer, with exceptions. Further, the bill specifies that the FAA must preserve state, local, and tribal authority to issue reasonable restrictions on the time, manner, and place of operation of drones below 200 feet above ground level. The bill includes additional exceptions to federal preemption requirements allowing for state, local, and tribal authorities to regulate specific drone activities. The FAA must also establish a process for the designation of authorized commercial routes, which must be at least 200 feet above ground level. The Department of Transportation must also establish a process for state, local, and tribal authorities to apply for a designation of complex airspace, which is an area that is at least 200 feet above ground level and includes at least one structure that exceeds 200 feet above ground level.