We demonstrated that by using a pump field with nonzero orbital angular momentum (OAM) in the polarization self-rotation squeezing process it is possible to generate a squeezed vacuum optical field with the matching OAM. We found a similar level of maximum quantum noise reduction for a first-order Laguerre-Gaussian pump beam and a regular Gaussian pump beam, even though the optimal operational conditions differed in these two cases. Also, we investigated the effect of self-defocusing on the level of the vacuum squeezing by simultaneously monitoring the minimum quantum noise level and the output beam transverse profile at various pump laser powers and atomic densities and found no direct correlations between the increased beam size and the degree of measured squeezing.