The physical properties of URhSn with quasi-kagome structure are studied using single-crystalline samples via electrical resistivity, magnetic susceptibility, heat capacity, thermal expansion, and high-field magnetization measurements. Remarkable magnetic anisotropy is found in the ferromagnetic (FM) state below TC=16K as well as in the ordered state between TC and TO=54K, where the easy and hard magnetization directions are the hexagonal  and [101¯0] axes. In the paramagnetic state, the magnetic susceptibility shows a Curie-Weiss behavior; the Weiss temperatures are positive and negative for  and [101¯0], respectively, indicating the presence of both FM and antiferromagnetic (AFM) correlations. The entropy release for 5f electrons is approximately Rln3 at TO. The thermal expansion coefficient is strongly anisotropic around TO between the hexagonal basal plane and the  axis, indicating its remarkable anisotropic magnetoelastic response and uniaxial stress dependences. Interestingly, the magnetic field response of the higher-temperature ordered state is unusual: TO(H) increases and the heat-capacity jump is enhanced with the magnetic field for H||. Based on the established thermodynamic evidence for the second-order transition at TO(H), a plausible scenario is the occurrence of a canted AFM ordering or a conical state under magnetic fields, which is stabilized when coupled with field-induced magnetic moments along the  axis. Another possibility is the occurrence of quadrupole ordering at TO(H).