We have studied the in-plane magnetic anisotropy in polycrystalline cobalt films, which were obliquely deposited by e-beam evaporation in UHV at T-s = 300 K. Three film series were studied, with average film thicknesses t = 15, 45 and 100 nm. For all cases, the incidence angle of the vapor beam with respect to the surface normal was alpha = 0, 30, 40, 50, 60 and 70 degrees. At normal incidence, the anisotropy and the coercive fields were found to be H-K = 15-25 Oe, and H-c similar or equal to 25 Oe, independent of the film thickness. In all series it has been observed that, as alpha increases, the easy axis of in-plane anisotropy switches from perpendicular to parallel with respect to the incidence plane of atoms during film deposition. For t = 15 nm, such a transition occurs at alpha(t) similar or equal to 70 degrees, whereas for larger values of t we found that alpha(t), similar or equal to 60 degrees. At constant film thicknesses, H-K and H-c increase with increasing alpha; the lower the film thickness, the sharper this effect, e.g. for alpha = 40 degrees, and t = 100, 45 and 15 nm, H-K similar or equal to 15, 30 and 150 Oe, respectively. We analyzed two possible contributions to this effect: the shape anisotropy and the magnetocrystalline anisotropy (texture). At low film thicknesses the former becomes dominant. In order to understand the effect of oblique incidence on the in-plane easy axis location we studied the polar plot of reduced remanence m(r) as a function of both the angle alpha (between the surface normal and the vapor beam) and the angle gamma (between the in-plane applied field and the normal to the incidence plane of atoms during deposition). The behavior of m(r)(alpha, gamma) for alpha = 10 degrees and 70 degrees is reminiscent of that predicted by the coherent-rotation Stoner and Wohlfarth model, although fallback processes are observed. We found that the films tend to be magnetically isotropic for alpha = 60 degrees, whereas they are highly anisotropic for alpha = 10 degrees.