In this paper we propose a Bayesian estimation approach for a spatial autoregressive logit specification. Our approach relies on recent advances in Bayesian computing, making use of Pólya-Gamma sampling for Bayesian Markov-chain Monte Carlo algorithms. The proposed specification assumes that the involved log-odds of the model follow a spatial autoregressive process. Pólya-Gamma sampling involves a computationally efficient treatment of the spatial autoregressive logit model, allowing for extensions to the existing baseline specification in an elegant and straightforward way. In a Monte Carlo study we demonstrate that our proposed approach significantly outperforms existing spatial autoregressive probit specifications both in terms of parameter precision and computational time. The paper moreover illustrates the performance of the proposed spatial autoregressive logit specification using pan-European regional data on foreign direct investments. Our empirical results highlight the importance of accounting for spatial dependence when modelling European regional FDI flows.