Detailed measurements of the in-plane resistivity were performed in a high-quality Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ ($x=0.065$) single crystal, in magnetic fields up to 9 T and with different orientations $theta$ relative to the crystal $c$ axis. A significant $rho(T)_{H,theta}$ rounding is observed just above the superconducting critical temperature $T_c$ due to Cooper pairs created by superconducting fluctuations. These data are analyzed in terms of a generalization of the Aslamazov-Larkin approach, that extends its applicability to high reduced-temperatures and magnetic fields. This method allows us to carry out a criterion-independent determination of the angular dependence of the upper critical field, $H_{c2}(theta)$. In spite of the relatively small anisotropy of this compound, it is found that $H_{c2}(theta)$ presents a significant deviation from the single-band 3D anisotropic Ginzburg-Landau (3D-aGL) approach, particularly for large $theta$ (typically above $sim60^o$). These results are interpreted in terms of the multiband nature of these materials, in contrast with other proposals for similar $H_{c2}(theta)$ anomalies. Our results are also consistent with an effective anisotropy factor almost temperature independent near $T_c$, a result that differs from the ones obtained by using a single-band model.
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