Semiconducting two-dimensional (2D) transition metal dichalcogenides (TMDs) are emerging as top candidates for post-silicon electronics. While most of 2D TMDs exhibit isotropic behavior, lowering the lattice symmetry could induce anisotropic properties, which are both scientifically interesting and potentially useful. Here, we present atomically thin rhenium disulfide (ReS2) flakes with a unique distorted 1T structure, which exhibit in-plane anisotropic properties. We fabricated mono- and few-layer ReS2 field effect transistors (FETs), which exhibit competitive performance with large current on/off ratios (~107) and low subthreshold swings (100 mV dec-1). The observed anisotropic ratio along two principle axes reaches 3.1, which is the highest among all known 2D semiconducting materials. Furthermore, we successfully demonstrated an integrated digital inverter with good performance by utilizing two ReS2 anisotropic FETs, suggesting the promising implementation of large-scale 2D logic circuits. Our results underscore the unique properties of 2D semiconducting materials with low crystal symmetry for future electronic applications.