  A rotating universe represented by the G\"{o}del metric in spacetimes with
Cartan torsion is investigated where the Cosmic Microwave Background Radiation
(CMBR) is computed from the G\"{o}del rotation of the universe and the spin
density of the spinning fluid in Einstein-Cartan gravity.The autoparallel
equation in Riemann-Cartan spacetime is shown to lead to the evolution equation
of the cosmological perturbation where the spin-rotation coupling is the source
of the growth of inhomogeneities.It is shown that temperature anisotropy is
within the limits of COBE constraint yielding a value of
$\frac{{\delta}T}{T}=10^{-7}$.This result opens the possibility of testing
Einstein-Cartan gravity from a cosmological experiment such as PLANCK or MAP.
