Several iterative schemes have been proposed to solve the coupled flow and geomechanics problem. In these schemes, the flow and mechanical problems are solved separately (i.e., decoupled), and an iterative coupling process is introduced to ensure convergence at each time step. Given the different time scales of the two processes, the flow problem can adopt a finer time step compared to the mechanics problem, leading to what is known as a multirate scheme. In this work, we derive a priori error estimates for the multirate fixed-stress split iterative coupling scheme. This approach generalizes the well-established fixed-stress split scheme by allowing the flow problem to take several fine time steps within a single coarse mechanics time step.