Combating Trafficking of Cuban Doctors Act of 2020 This bill requires the Department of State to reinstate the Cuban Medical Professional Parole program to authorize the admission into the United States of Cuban medical personnel conscripted to study or work in a third country under the direction of the Cuban government. The State Department must also submit an annual report and determination on the international trafficking of Cuban medical personnel, as well as report on and make recommendations related to the role of the Pan American Health Organization in this practice.