As an alternative to correlation-based techniques widely used in conventional speckle metrology, we propose a new technique that makes use of phase singularities in the complex analytic signal of a speckle pattern as indicators of local speckle displacements. The complex analytic signal is generated by vortex filtering the speckle pattern. Experimental results are presented that demonstrate the validity and the performance of the proposed optical vortex metrology with nano-scale resolution.