  We use data from Supernovae (SNIa) Scolnic sample, from Baryonic Acoustic
Oscillations (BAO), and from cosmic chronometers measurements of the Hubble
parameter (CC), alongside arguments from Big Bang Nucleosynthesis (BBN), in
order to extract constraints on Myrzakulov $F(R,T)$ gravity. This is a
connection-based theory belonging to the Riemann-Cartan subclass, that uses a
specific but non-special connection, which then leads to extra degrees of
freedom. Our analysis shows that both considered models lead to $\sim 1 \sigma$
compatibility in all cases. For the involved dimensionless parameter we find
that it is constrained to an interval around zero, however the corresponding
contours are slightly shifted towards positive values. Furthermore, applying
the AIC, BIC and the combined DIC criteria, we deduce that both models present
a very efficient fitting behavior, and are statistically equivalent with
$\Lambda$CDM cosmology, despite the fact that Model 2 does not contain the
latter as a limit. Finally, we use the obtained parameter region and we
reconstruct the corresponding dark-energy equation-of-state parameter as a
function of redshift. As we show, Model 1 is very close to $\Lambda$CDM
scenario, while Model 2 resembles it at low redshifts, however at earlier times
deviations are allowed.
