We have developed a mechanical absolute-rotation sensor capable of resolving ground rotation angle of less than 1 nrad/√Hz above 30 mHz and 0.2 nrad/√Hz above 100 mHz about a single horizontal axis. The device consists of a meter-scale beam balance, suspended by a pair of flexures, with a resonance frequency of 10.8 mHz. The center of mass is located 3 μm above the pivot, giving an excellent horizontal displacement rejection of better than 3 × 10(-5) rad/m. The angle of the beam is read out optically using a high-sensitivity autocollimator. We have also built a tiltmeter with better than 1 nrad/√Hz sensitivity above 30 mHz. Co-located measurements using the two instruments allowed us to distinguish between background rotation signal at low frequencies and intrinsic instrument noise. The rotation sensor is useful for rotational seismology and for rejecting background rotation signal from seismometers in experiments demanding high levels of seismic isolation, such as Advanced Laser Interferometer Gravitational-wave Observatory.