Cell migration is frequently modeled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing, and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can "swap" its position with another agent in its neighborhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behavior of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyze the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.