Keep STEM Talent Act of 2023 This bill addresses issues relating to non-U. S. nationals ( aliens under federal law) with advanced degrees in a science, technology, engineering, or mathematics (STEM) field, including exempting certain such individuals from direct limitations on the number of immigrant visas granted per year. To be exempt from the annual numerical limitations on immigrant visas, the individual must (1) have earned a master's level or higher degree in certain STEM fields while in the United States attending an accredited higher education institution, (2) be employed (or have an offer) to perform work directly related to the degree and earn higher than the median wage for that occupation, and (3) meet certain labor certification requirements. The bill also allows an individual seeking a nonimmigrant F-1 (student) visa for an advanced STEM degree to obtain the nonimmigrant visa even if the individual seeks lawful permanent resident status. (Generally, an individual may be denied a nonimmigrant visa if the individual actually intends to seek immigrant status, unless dual intent is allowed for that visa.) Under this bill, to be approved for an F-1 visa for an advanced STEM degree, the applicant must apply for the visa before beginning the advanced degree program. The bill also requires an individual who is inside the United States and applying for an F-1 visa for an advanced STEM degree to undergo the same vetting (e.g., verifying academic credentials and undergoing background checks) as an individual applying from outside the United States.