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The target in an augmented reality (AR) interface is often located in the distance and outside the initial AR viewport, requiring the user to rotate the AR device, instead of translating it, to complete the search and selection of the target. In order to quantitatively analyze rotating the AR device in the AR interface in the selection of a target located outside the initial visual window, we propose and experimentally verify a quantitative model based on angle measurement under two selection techniques: with and without cursor. The results show that the model proposed in this paper can accurately describe the interactive process when a rotating AR device completes the target selection task. With cursor angle measurement achieves a model fitting value of R² = 0.937, and without cursor angle measurement achieves a model fitting value of R² = 0.915; hence, good modeling of user performance in AR selection tasks is achieved.