Talk to the student about the problem before you change your policies. You may find that there is a fixable reason for the tardiness. Perhaps the student gets anxious before class and has panic attacks. Maybe she's fighting traffic and needs to leave home earlier. A medical condition that requires frequent bathroom visits, medication or injections could cause a student to be late, particularly if she's darting from one class to the next. If a student has a valid reason, discuss ways to minimize the issue and reduce disruptions.
Give students a positive reason to come to class by incorporating test material that's not in the book into your lectures. This rewards students for arriving to class on time, without directly punishing latecomers. You might also want to go over bonus material for the test. For example, add a 10-point bonus to the test and discuss the answer to the question during the first few minutes of class. Make sure students know you'll be discussing this material early in the class session.
Punitive attendance policies punish students with valid reasons for their absences or medical conditions, but a positive attendance policy rewards students who are on time without penalizing latecomers. Try offering a few bonus points on a student's final grade if they're regularly on time for class. Alternatively, you might offer a boost of a point or two on a test grade every few days for students who are in class on time.
If a student persists in coming to class late even when it harms her grade, you don't have to resort to instituting penalties to minimize disruptions. Try putting a few chairs next to the door and putting a trash can in front of the door so that it doesn't slam shut, disrupting other students.