  The recently reported measurement of the $W$-boson mass by CDF-II
collaboration is significantly heavier than that of the Standard Model
prediction. We study this anomaly in the scale invariant
Two-Higgs-Doublet-Model (SI-2HDM) with a $\mathbb{Z}_2$ symmetry to avoid the
flavor-changing-neutral-current (FCNC). In this scenario the Higgs particle is
the classically massless scalon in the SI-2HDM gaining its mass by radiative
corrections, hence being naturally light. Moreover, because of the scale
symmetry the model is more predictive respect to the generic 2HDM. We show that
the oblique parameters depending on the masses of the charged and CP-even
(CP-odd) neutral scalar components of the SI-2HDM denoted respectively by
$M_{H^\pm}$ and $M_h$ ($M_A$), are large enough to accommodate the $W$-boson
mass anomaly in the model. There are as well viable regions in the mass
spectrum of the SI-2HDM that evade the experimental bounds from colliders on
the charged Higgs and neutral scalars.
