This paper reports slow-wave substrate integrated waveguide (SW-SIW) with rotary tensor unit cells and its applications to filters design. The proposed cross-shaped tensor unit cell can show anisotropic guided-wave parameters of interest, namely its equivalent permittivity and permeability along the transverse direction are different from those along the longitudinal direction. Hence, as rotating the tensor unit cells, equivalent permittivity and permeability of the SW-SIW will be varied, thus its guided-wave properties can be adjusted flexibly. Moreover, the proposed SW-SIW is utilized to constitute slow-wave cavity for filters design. By rotating the tensor unit cells with various angles, equivalent permeability and permittivity of the cavity can be changed as well, which will further influence the cavity’s resonant frequency differently. Experimental results of the proposed SW-SIW cavity filters are in good agreement with simulations, which indicate that the filters’ resonance and coupling properties can be adjusted by rotating the tensor unit cells.