Summary In randomized controlled trials with non-adherence, instrumental variable (IV) methods are frequently used to report the complier average causal effect. With binary outcomes, many of the available IV estimation methods impose distributional assumptions. We develop a randomization-inference-based method of IV estimation for binary outcomes. The method is non-parametric and is based on Fisher's exact test, and estimates can be easily calculated from a set of 2×2 or 2×2×2 tables. Although we retain the standard IV identification assumptions for confidence regions and point estimates, the IV estimand under randomization inference is sample specific and does not assume that the randomized controlled trials participants are a random sample from the target population. We illustrate the method with the ‘IMPROVE’ trial that compares emergency endovascular versus open surgical repair for patients with ruptured aortic aneurysms.