Linkage errors in probabilistically matched data sets can cause biases in the estimation of regression coefficients. This article proposes an approach to obtain consistent estimates and valid inference that relies on instrumental variables. The novelty of the method is to show that instrumental variables arise naturally in the course of probabilistic record linkage thereby allowing for off-the-shelf implementation. Relative to existing approaches, the instrumental variable approach does not require integration of the record linkage and regression analysis steps, the estimation of complex models of linkage error, or computationally expensive methods to estimate standard errors. The instrumental variables approach performs well in Monte Carlo simulations of an environment highlighting a many-to-one linkage problem.