The newly found superconductivity in infinite-layer nickelate superconducting films has attracted much attention, because their crystalline and electronic structures are similar to high-$T_c$ cuprate superconductors. The upper critical field can provide much information on superconductivity, but detailed experimental data are still lacking in these films. Here we present temperature and angle dependence of resistivity measured under different magnetic fields ($H$) in Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$ thin films. The onset superconducting transition occurs at about 16.2 K at 0 T. Temperature dependent upper critical fields determined by using a criterion very close to the onset transition show a clear negative curvature near the critical transition temperature, which is explained as the consequence of the paramagnetically limited effect on superconductivity. The temperature dependent anisotropy of the upper critical field is obtained from resistivity data, which yields a value decreasing from 3 to 1.2 with lowering temperature. This can be explained by a variable contribution from the orbital limit effect on upper critical field. The angle dependent resistivity at a fixed temperature and different magnetic fields cannot be scaled to one curve, which deviates from the prediction of the anisotropic Ginzburg-Landau theory. However, at low temperatures, the increased resistivity by magnetic field can be scaled by the parameter $H^beta |costheta|$ ($1<beta<6$) with $theta$ the angle enclosed between $c$-axis and the applied magnetic field. As the first detailed study on the upper critical field of the nickelate thin films, our results clearly indicate a small anisotropy and paramagnetically limited effect of superconductivity in nickelate superconductors.
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