The Harvard admissions department indicates on its FAQ page that it doesn't have specific minimum standardized test score requirements. However, students admitted to the school typically fall within a range of relatively high scores. According to Harvard, the typical ACT score range for students admitted to Harvard is 33 to 35.
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Roughly 25 percent of students admitted to Harvard have ACT scores below 33. Using a statistical normal distribution, Harvard likely only admits students with ACT scores above 30. As unlikely as it is to gain admission with a lower score, those admitted will typically need an above-average performance on other application materials, including your grades, activities and recommendation letters. Students can also take the SAT as opposed to the ACT.
Harvard reports that admitted students normally have scores between 710 to 770 on the SAT Evidence-Based Reading and Writing and between 750 and 800 on SAT Math. 71% submitted SAT scores in 2019.
All applicants, regardless of which general exam they choose to take, must complete two SAT Subject Tests.