Measuring the angular displacement of a mechanical oscillator is a ubiquitous task; however, the multimode nature of angular optomechanical coupling makes coherent signal enhancement challenging. Here we demonstrate coherently enhanced angular displacement readout with an integrated guided mode resonance (GMR) structure, applying it to precision readout of a nanomechanical oscillator. Specifically, we fabricate subwavelength gratings into 100-nm-thick Si₃N₄ membranes and record their vibration by direct transmission measurements. The narrow linewidth ≈ 2.5 mrad of the GMR enables a shot-noise-limited displacement imprecision of 10⁻⁹ rad/√Hz with nanowatts of optical power, sufficient to resolve the thermal motion of a Q≈ 10⁶ torsion mode with a signal-to-noise ratio of 47 dB. Control experiments based on polarization and wavelength detuning confirm that the measured signal arises from GMR-mediated transduction. These results establish guided-mode resonance as an on-chip approach to angular displacement readout in quantum optomechanical sensors.