  Present gravitational wave detectors are based on the measurement of linear
displacement in stable optical cavities. Here, we instead suggest the
measurement of the twist of a chiral mechanical element induced by a
gravitational wave. The induced twist rotates a flat optical mirror on top of
this chiral element, leading to the deflection of an incident laser beam. This
angle change is enhanced by multiple bounces of light between the rotating
mirror and an originally parallel nearby fixed flat mirror. Based on detailed
continuum-mechanics calculations, we present a feasible design for the chiral
mechanical element including the rotating mirror. Our approach is most useful
for signals in the frequency band 1 -- 100 kHz where we show that fundamental
metrological limits would allow for smaller shot noise in this setup in
comparison to the detection of linear displacement. We estimate a gravitational
wave strain sensitivity between 10^{-21}/\sqrt{Hz} and 10^{-23}/\sqrt{Hz} at
around 10 kHz frequency. When appropriately scaling the involved geometrical
parameters, the strain sensitivity is proportional to frequency.
