  We study inflation in the framework of $f(T)$-gravity in the presence of a
canonical scalar field. After reviewing the basic equations governing the
background cosmology in $f(T)$-gravity, we turn to study the cosmological
perturbations and obtain the evolutionary equations for the scalar and tensor
perturbations. Solving those equations, we find the power spectra for the
scalar and tensor perturbations. Then, we consider a power-law form for the
$f(T)$ function in the action and examine the inflationary models with the
power-law and intermediate scale factors. We see that in contrast with the
standard inflationary scenario based on the Einstein gravity, in the considered
$f(T)$-gravity scenario, the power-law and intermediate inflationary models can
be compatible with the observational results of Planck 2015 at 68\% CL. In our
$f(T)$-gravity setting, the potentials responsible for both the power-law and
intermediate inflationary models have the power-law form $V(\phi ) \propto
{\phi ^m}$ but the power $m$ is different for them. Therefore, we can refine
some of power-law inflationary potentials in the framework of $f(T)$-gravity
while they are disfavored by the observational data in the standard
inflationary scenario. Interestingly enough, the self-interacting quartic
potential $V(\phi ) \propto {\phi ^4}$ which has special reheating properties,
can be consistent with the Planck 2015 data in our $f(T)$-gravity scenario
while it is ruled out in the standard inflationary scenario.
