Existing work on appointment scheduling assumes that appointment times cannot be updated once they have been assigned.However, advances in communication technology and the adoption of online (as opposed to in-person) appointments make it possible for appointments to be flexible. In this paper, we describe an intra-day dynamic rescheduling model that adjusts upcoming appointments based on observed no-shows. We formulate the problem as a Markov Decision Process in order to compute the optimal pre-day schedule and the optimal policy to update the schedule for every scenario of no-shows. We also propose an alternative formulation based on the idea of 'atomic' actions that can solve for the optimal policy more efficiently. Based on a numerical study, we estimate that using intra-day dynamic rescheduling can lead to a 5-7% decrease in expected cost when compared to static scheduling.