Pre-trained large language models (LMs) struggle to perform logical reasoning reliably despite advances in scale and compositionality. In this work, we tackle this challenge through the lens of symbolic programming. We propose DSR-LM, a Differentiable Symbolic Reasoning framework where pre-trained LMs govern the perception of factual knowledge, and a symbolic module performs deductive reasoning. In contrast to works that rely on hand-crafted logic rules, our differentiable symbolic reasoning framework efficiently learns weighted rules and applies semantic loss to further improve LMs. DSR-LM is scalable, interpretable, and allows easy integration of prior knowledge, thereby supporting extensive symbolic programming to robustly derive a logical conclusion. The results of our experiments suggest that DSR-LM improves the logical reasoning abilities of pre-trained language models, resulting in a significant increase in accuracy of over 20% on deductive reasoning benchmarks. Furthermore, DSR-LM outperforms a variety of competitive baselines when faced with systematic changes in sequence length.