Faculty may offer this as an option to students. However, if the student has a disability-related need for a make-up exam (the student's assigned Disability Specialist can verify if needed), then the student has a right to take a make-up exam.
You can choose to administer the same exam to the student as the exam the class has already taken. Some instructors ask students to sign an academic integrity agreement verifying that the student has not accessed the already-administered exam or discussed it with others.
You can also choose to offer the student an alternate exam of the same format and difficulty as the original exam.