The cosmological model is at present not tested between the redshift of the farthest observed supernovae (z~1.4) and that of the Comsic Microwave Background (z~1,100). Here we introduce a new method to measure the cosmological parameters: we show that quasars can be used as “standard candles” by employing the non-linear relation between their intrinsic UV and X-ray emission as an absolute distance indicator. We built a sample of ~900 quasars with available UV and X-ray observations, and produced a Hubble diagram up to z~6.3, from which we derived Omega_M=0.24+0.16-0.09. When used in combination with supernovae, our data provide Omega_M=0.25±0.05 and Omega_Lambda=0.67±0.08. The application of this method to forthcoming, larger quasar samples, will provide tight constraints on the dark energy equation of state.