We have studied the temperature dependence of low-field magnetoresistance and current-voltage characteristics of a low-angle bi-crystal grain boundary junction in perovskite manganite La_{2/3}Sr_{1/3}MnO_3 thin film. By gradually trimming the junction we have been able to reveal the non-linear behavior of the latter. With the use of the relation M_{GB} propto M_{bulk}sqrt{MR^*} we have extracted the grain boundary magnetization. Further, we demonstrate that the built-in potential barrier of the grain boundary can be modelled by V_{bi}propto M_{bulk}^2 - M_{GB}^2. Thus our model connects the magnetoresistance with the potential barrier at the grain boundary region. The results indicate that the band-bending at the grain boundary interface has a magnetic origin.
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