  We investigate the evolution of scalar perturbations in $f(T)$ teleparallel
gravity and its effects on the cosmic microwave background (CMB) anisotropy.
The $f(T)$ gravity generalizes the teleparallel gravity which is formulated on
the Weitzenb\"ock spacetime, characterized by the vanishing curvature tensor
(absolute parallelism) and the non-vanishing torsion tensor. For the first
time, we derive the observational constraints on the modified teleparallel
gravity using the CMB temperature power spectrum from Planck's estimation, in
addition to data from baryonic acoustic oscillations (BAO) and local Hubble
constant measurements. We find that a small deviation of the $f(T)$ gravity
model from the $\Lambda$CDM cosmology is slightly favored. Besides that, the
$f(T)$ gravity model does not show tension on the Hubble constant that prevails
in the $\Lambda$CDM cosmology. It is clear that $f(T)$ gravity is also
consistent with the CMB observations, and undoubtedly it can serve as a viable
candidate amongst other modified gravity theories.
