We propose a robust estimator for functional autoregressive models. This estimator, the Depth-based Least Squares (DLS) estimator, down-weights the influence of outliers by using the functional outlyingness as a centrality measure. The DLS estimator consists of two steps: identifying the outliers with a functional boxplot based on a defined depth, then down-weighting the outliers using the functional outlyingness. We prove that the influence function of the DLS estimator is bounded. Through a Monte Carlo study, we show that the DLS estimator performs better than the PCA and robust PCA estimators, which are the most commonly used.