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.
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