Not a mandatory one.
There is an advisory one for students without calculus in high school (or too-low score on AP/IB/A-level exam) considering whether they are ready for MATH 1A: https://math.berkeley.edu/courses/choosing/placement-exam
There are also the old MATH 1A, 1B, etc. final exams at https://tbp.berkeley.edu/courses/math/ for those who want to check their knowledge when deciding whether to take advanced placement.