Keep STEM Talent Act of 2021 This bill exempts certain aliens with advanced degrees in a science, technology, engineering, or mathematics (STEM) field from direct limitations on the number of immigrant visas granted per year. Specifically, the alien 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 a job offer) in a field related to the degree and earn at least the median wage for that occupation, and (3) meet certain labor certification requirements. The bill also allows an alien seeking a nonimmigrant F-1 (student) visa to obtain an advanced STEM degree to have dual intent. Specifically, such an alien may obtain the nonimmigrant visa or change nonimmigrant status even if the alien intends to seek lawful permanent resident status. (Generally, an alien may be denied a nonimmigrant visa if the alien actually intends to seek immigrant status, unless dual intent is allowed for that type of visa.)