Simulation-based inference (SBI) has emerged as a family of methods for performing inference on complex simulation models with intractable likelihood functions. A common bottleneck in SBI is the construction of low-dimensional summary statistics of the data. In this respect, time-series data, often being high-dimensional, multivariate,and complex in structure, present a particular challenge. To address this we introduce deep signature statistics, a principled and automated method for combining summary statistic selection for time-series data with neural SBI methods. Our approach leverages deep signature transforms, trained concurrently with a neural density estimator, to produce informative statistics for multivariate sequential data that encode important geometric properties of the underlying path. We obtain competitive results across benchmark models.