Demountable structures are designed to reduce carbon emissions and energy consumption in the construction sector by reusing structural components. This paper focuses on an anchoring coupler with demountable property used in the demountable precast concrete structure. The shear resistance of the anchoring coupler at varying shear positions was investigated, considering the influence of installation and fabrication errors in actual projects. Firstly, several shear tests of the anchoring coupler were conducted. The ultimate capacities and failure modes of anchoring couplers with varying shear positions were obtained. The bearing capacity of the anchoring coupler without the gap between the beam and column is about 1.34 times that with 45 mm gap. The shear model of the anchoring coupler was fitted by the bilinear curves. Secondly, the numerical model of the anchoring coupler was established and verified. And the influence of the shear position on the ultimate strength was further analyzed by parametric analysis. A simplified calculation method of the shear resistance of the anchoring coupler with varying shear positions was proposed. The design equation for predicting the tension-shear interaction was recommended, considering the similarity between the anchoring coupler and conventional bolt. The aim is to provide theoretical guidance for the safety design of the anchoring coupler and optimize the beam-column connection, which is conducive to expanding the application of the demountable precast concrete structure.