Small inner working angle coronagraphs, like the vortex phase mask, are essential to exploit the full potential of ground-based telescopes in the context of exoplanet detection and characterization. However, the drawback of this attractive feature is a high sensitivity to pointing errors, which degrades the performance of the coronagraph. We propose a tip-tilt retrieval technique based on the analysis of the final coronagraphic image, hereafter called Quadrant Analysis of Coronagraphic Images for Tip-tilt Sensing (QACITS). Under the assumption of small phase aberrations, we show that the behaviour of the vortex phase mask can be simply described from the entrance pupil to the Lyot stop plane by Zernike polynomials. This convenient formalism is used to establish the theoretical basis of the QACITS technique. Simulations have been performed to demonstrate the validity and limits of the technique, including the case of a centrally obstructed pupil. The QACITS technique principle is further validated by experimental results in the case of an unobstructed circular aperture. The typical configuration of the Keck telescope (24% central obstruction) has been simulated with additional high order aberrations. In these conditions, our simulations show that the QACITS technique is still adapted to centrally obstructed pupils and performs tip-tilt retrieval with a precision of $5 \times 10^{-2}$ {\lambda}/D when wavefront errors amount to {\lambda}/14 rms and $10^{-2}$ {\lambda}/D for {\lambda}/70 rms errors (with {\lambda} the wavelength and D the pupil diameter). The implementation of the QACITS technique is based on the analysis of the scientific image and does not require any modification of the original setup. Current facilities equipped with a vortex phase mask can thus directly benefit from this technique to improve the contrast performance close to the axis.
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