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Dark matter halos acquire angular momentum through tidal torques in the linear regime and generate vorticity after shell crossing in the non-linear regime. While these processes are well characterized on halo scales, the degree to which coherent rotational asymmetry persists on intermediate mesoscopic scales from 10 to 50 megaparsecs remains uncertain. In this methodological study, we define the observable and characterize its sensitivity on 20 to 50 megaparsec domains, a conservative operational range where sensitivity and null-test stability are strongest. We develop a statistical framework for detecting such coherence in weak-lensing shear maps using a log-polar power spectrum estimator ($B_{m \le 2}$). This estimator isolates low-order azimuthal deviations in the stacked shear field, explicitly retaining angular information normally suppressed by standard azimuthally averaged two-point statistics. We treat an isotropic Gaussian shear field as a maximum-entropy baseline, where coherent low-order structure represents a measurable deviation from that expectation. To interpret these measurements, we define a domain-averaged kinematic proxy, K omega, derived from the Raychaudhuri equation, quantifying the potential contribution of vorticity to the local expansion history. We characterize the estimator sensitivity using controlled analytic mock maps and validate the pipeline against full-sky Lambda cold dark matter ray-tracing simulations to establish a background noise floor. The resulting framework provides a falsifiable method to assess whether the dark sector exhibits measurable rotational support at mesoscopic scales using projected weak-lensing data.