Drug Cartel Terrorist Designation Act This bill directs the Department of State to report to Congress on specified Mexican drug cartels and determine whether they qualify as foreign terrorist organizations under the Immigration and Nationality Act. The State Department shall explain in detail its reasoning if it concludes that any of the specified cartels do not qualify. The report shall analyze the Reynosa/Los Metros faction of the Gulf Cartel, the Jalisco New Generation Cartel, and the Cartel Del Noreste faction of Los Zetas.