  As one of the possible extensions of Einstein's General Theory of Relativity,
it has been recently suggested that the presence of spacetime torsion could
solve problems of the very early and the late-time universe undergoing
accelerating phases. In this paper, we use the latest observations of
high-redshift data, coming from multiple measurements of quasars and baryon
acoustic oscillations, to phenomenologically constrain such cosmological model
in the framework of Einstein-Cartan (EC) endowed with spacetime torsion. Such
newly compiled quasar datasets in the cosmological analysis is crucial to this
aim, since it will extend the Hubble diagram to high-redshift range in which
predictions from different cosmologies can be distinguished. Our results show
that out of all the candidate models, the torsion plus cosmological constant
model is strongly favoured by the current high-redshift data, where torsion
itself would be expected to yield the current cosmic acceleration. Specially,
in the framework of Friedmann-like cosmology with torsion, the determined
Hubble constant is in very good agreement with that derived from the Planck
2018 CMB results. On the other hand, our results are compatible with zero
spatial curvature and there is no significant deviation from flat spatial
hypersurfaces. Finally, we check the robustness of high-redshift observations
by placing constraints on the torsion parameter $\alpha$, which is strongly
consistent with other recent works focusing on torsion effect on the primordial
helium-4 abundance.
