Higher Education Marijuana Research Act of 2023 This bill establishes programs and requirements to support marijuana research by institutions of higher education. For example, the bill requires the Drug Enforcement Administration (DEA) to report on the number and status of licenses awarded to entities seeking to manufacture controlled substances and to prioritize institutions of higher education and state or local government entities when awarding such licenses. The DEA must also establish an Office of University Relations to support the ability of researchers and institutions of higher education to obtain these licenses. The bill also specifies that institutions of higher education may obtain marijuana for research purposes from government entities of the state or tribal area in which they are located if doing so is legal in that state or tribal area, despite federal law. Further, any individual or institution of higher education may participate in such research without losing federal funds. Finally, the National Institutes of Health must establish (1) a working group to recommend ways to streamline the registration process for marijuana research, and (2) a grant program to support research into medical marijuana. The Department of Agriculture must establish a grant program to support research into marijuana agriculture.