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In this work, we explore the possibility of using artificial neural networks to impose constraints on teleparallel gravity and its $f(T)$ extensions. We use the available Hubble parameter observations from cosmic chronometers and baryon acoustic oscillations from different galaxy surveys. We discuss the procedure for training a network model to reconstruct the Hubble diagram. Further, we describe the procedure to obtain $H'(z)$, the first order derivative of $H(z)$, using artificial neural networks which is a novel approach to this method of reconstruction. These analyses are complemented with further studies on the impact of two priors which we put on $H_0$ to assess their impact on the analysis, which are the local measurements by the SH0ES team ($H_0^{\text{R20}} = 73.2 \pm 1.3$ km Mpc$^{-1}$ s$^{-1}$) and the updated TRGB calibration from the Carnegie Supernova Project ($H_0^{\text{TRGB}} = 69.8 \pm 1.9$ km Mpc$^{-1}$ s$^{-1}$), respectively. Additionally, we investigate the validity of the concordance model, through some cosmological null tests with these reconstructed data sets. Finally, we reconstruct the allowed $f(T)$ functions for different combinations of the observational Hubble data sets. Results show that the $Λ$CDM model lies comfortably included at the 1$σ$ confidence level for all the examined cases.