Orozco received a bachelor's degree in Chemistry from the Autonomous University of Chihuahua and a master and doctorate's degree in Cell biology from Centro de Investigación y Estudios Avanzados (Cinvestav IPN)(1977, 1981). She is Full Professor of the Department of Infectomics and Experimental Pathogenesis at Cinvestav. She has been visitor professor in Harvard University, Weizmann Institute and other international institutions. She is Emeritus Professor of Cinvestav and National Emeritus Researcher. Orozco is co-founder of the Center for Scientific Research and Applied Technology of National Polythecnic Institute, and, in December 2006, she founded and directed the Institute for Science and Technology of Mexico City.She also  She has been international fellow of Howard Hughes Medical Institute for 10 years. As a visiting scholar, she has lectured at Harvard University and the Weizmann Institute of Science.
She was also president of the Universidad Autónoma de la Ciudad de México (UACM), where she tried to improve the quality of higher education. For this reason she faced severe aggressions from the radical groups. In spite of this, she decided do not deliver UACM to the violent groups in Mexico City, and she did not resigned. However, these groups take UACM and tried to destroy all the work done by Orozco.