  The direct detection of gravitational waves (GWs) opened a new chapter in the
modern cosmology to probe possible deviations from the general relativity (GR)
theory. In the present work, we investigate for the first time the modified GW
form propagation from the inspiraling of compact binary systems within the
context of $f(T)$ gravity in order to obtain new forecasts/constraints on the
free parameter of the theory. First, we show that the modified waveform differs
from the GR waveform essentially due to induced corrections on the GWs
amplitude. Then, we discuss the forecasts on the $f(T)$ gravity assuming
simulated sources of GWs as black hole binaries, neutron star binaries and
black hole - neutron star binary systems, which emit GWs in the frequency band
of the Advanced LIGO (aLIGO) interferometer and of the third generation
Einstein Telescope (ET). We show that GWs sources detected within the aLIGO
sensitivity can return estimates of the same order of magnitude of the current
cosmological observations. On the other hand, detection within the ET
sensitivity can improve by up to 2 orders of magnitude the current bound on the
$f(T)$ gravity. Therefore, the statistical accuracy that can be achieved by
future ground based GW observations, mainly with the ET detector (and planed
detectors with a similar sensitivity), can allow strong bounds on the free
parameter of the theory, and can be decisive to test the theory of gravitation.
