We have experimentally generated higher order optical vortices and scattered them through a ground glass plate that results in speckle formation. Intensity autocorrelation measurements of speckles show that their size decreases with increase in the order of the vortex. It implies increase in angular diameter of the vortices with their order. The characterization of vortices in terms of their annular bright ring also helps us to understand these observations. The results may find applications in stellar intensity interferometry and thermal ghost imaging.