  We study the dynamics of inflation in a generalized scalar-torsion gravity
scenario by assuming a canonical scalar field non-minimally coupled to torsion
with a Galileon-type self-interaction. After obtaining the field equations for
a flat FRW background, we derive the second order action for both scalar and
tensor perturbations to compute the power spectra of primordial fluctuations.
As particular models, we studied at first, a power-law form of coupling
function $F(x)=1+\xi x^{2}/2$, with $x\equiv \phi/M_{pl}$, and a monomial
scalar field potential $V(x)=\lambda x^{n}/n$ which is ruled out at $2\sigma$
level by current observational data for $n\geq 2$. Under slow-roll
approximation we obtain analytical expressions for the background as well as
perturbative dynamics, and we show that the predictions of the model are
consistent with current Planck 2018 constraints on the spectral index $n_{s}$
and the tensor-to-scalar ratio $r$ through the $n_s-r$ plane. Accordingly, this
model is in agreement with current observational bounds only within the $95\%$
C.L. region in the case of chaotic quadratic inflation ($n=2$), whereas that
for the other monomial potentials such as $n=4/3$, $n=1$ and $n=2/3$, it is
found that they are even more favoured, overlapping their results with the
$68\%$ C.L. region from last Planck data. Secondly, we studied a model in which
the presence of both non-minimal coupling to gravity and the Galileon
non-linear self-interaction $\gamma (\partial \phi)^2 \Box{\phi}$ leads to a
suppression of the tensor-to-scalar ratio compared to those predicted in the
standard scenario, then predicting $0.024\lesssim r\lesssim 0.069$. This result
allows us to reconcile chaotic quadratic inflation with current Planck data up
to the $68\%$ C.L. region.
