Most mountain belts on Earth show some degree of curvature in plan view, from a slight bend to horseshoe shapes. Such curvatures may occur on different scales, from individual thrust sheets to entire plate boundaries. Curvature may be acquired by vertical-axis rotation during or after orogenesis, or reflect primary lateral variations in shortening directions or physiographical features. Quantifying the amount of vertical-axis rotations of plan-view curvature is therefore helpful to our understanding of orogenesis, geodynamics, and paleogeography. The orocline test assesses to what extent vertical-axis rotations have played a role in the acquisition of an orogen’s curvature. The test quantifies through linear regression the relationships between changes in structural trends and the orientations of a geologic fabric. However, the current mathematical approaches to the orocline test show potential biases. In this paper we aim to overcome such biases by developing a novel orocline test that applies total least squares (TLS) regression combined with a novel approach to bootstrapping. This bootstrap TLS orocline test can be used with all types of directional data acquired from structural geology, paleomagnetism, or sedimentology. It quantifies, for the first time, secondary curvature with confidence bands. We also provide several graphical and analytical tests to evaluate the statistical significance of the result. An open source online application implementing this method is available for use on www.paleomagnetism.org. We illustrate the use of the methodology by reanalyzing published data sets from two well-known oroclines in the Cantrabrian (northwest Iberia) and Aegean (Greece) regions.