  We use a combination of observational data in order to reconstruct the free
function of f(T) gravity in a model-independent manner. Starting from the
data-driven determined dark-energy equation-of-state parameter we are able to
reconstruct the f(T) form. The obtained function is consistent with the
standard {\Lambda}CDM cosmology within 1{\sigma} confidence level, however the
best-fit value experiences oscillatory features. We parametrise it with a
sinusoidal function with only one extra parameter comparing to {\Lambda}CDM
paradigm, which is a small oscillatory deviation from it, close to the best-fit
curve, and inside the 1{\sigma} reconstructed region. Similar oscillatory
dark-energy scenarios are known to be in good agreement with observational
data, nevertheless this is the first time that such a behavior is proposed for
f(T) gravity. Finally, since the reconstruction procedure is completely
model-independent, the obtained data-driven reconstructed f(T) form could
release the tensions between {\Lambda}CDM estimations and local measurements,
such as the H0 and {\sigma}8 ones.
