We demonstrate both experimentally and numerically a new type of hole array structure that exhibits optically diffractive focusing phenomenon. The hole arrays are designed based on the aperiodic Vogel spirals. In contrast to periodic and quasi-periodic hole arrays that contain discrete Bragg peaks in reciprocal space, the Vogel spiral hole arrays have particularly continuous Fourier components with circular symmetry, which enables optical wave focusing into a diffraction-limited hotspot for a wide range of incident wavelengths. We further demonstrate that the diffracted fields contain local orbital angular momentum (OAM) leading to rotations of the diffractive circular rings around the center, although the total OAM is zero.