Conventional measurements of optical chirality are based on the response difference of material to the left- and right-handed circularly polarized light. Circularly polarized state of light carries spin angular momentum (SAM) of photons. Orbital angular momentum (OAM) introduces a new degree of freedom of light. For chiral measurement, OAM of photons can be exploited in new methods for the study of the chirality of substances. In this review, starting with the basic concepts of SAM, OAM and optical chirality, the chirality measurement methods based on the OAM of photons in recent years are summarized. These latest developments show that the chiral signal of conventional circular dichroism can be enhanced by the light with OAM. On the other hand, based on the spin-orbit coupling effect and the high order interaction between light field and electric quadrupole of molecules, chiral signals can be measured by directly switching the sign of OAM of photons. In addition, light with high-order OAM state is helpful to improve the chiral response of particles with size larger than wavelength. Finally, the recent progress on spatiotemporal optical vortex and its potential applications on chiral measurements are also presented.