In this article, we consider a random access scheme for an indoor Internet of Things (IoT) framework that uses optical wireless communication (OWC). We focus on a Slotted ALOHA (SA)-based solution where a number of OWC IoT users contend to send data to a central OWC receiver. In any given slot, and for a randomly selected active user, we consider the reliability of decoding the user's data packet at the receiver. This is done by deriving the signal-to-noise-and-interference-ratio (SINR) statistics from a randomly chosen user and evaluating the probability that the user's SINR is below a given threshold. By placing our analysis in the context of an indoor OWC IoT uplink setup, and employing the standard OWC channel model, we investigate the trade-offs between the reliability and the OWC system parameters such as the cell area or the transmitter's semi-angle. We obtain valuable insights into the design of an SA-based random access solution for a typical indoor OWC cell.