In a move that could boost student test scores, the ACT plans to let students retake portions of the college entrance exam.

Beginning next September, students will be allowed to retake sections of the exam if they don’t like their score, the testing body said. In the past, students had to retake the entire exam. Colleges will see all of the student’s scores from a single sitting and any additional scores from retakes that students want to include.

“We’re...