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We use galaxy-galaxy lensing data to test general relativity and $f(T)$gravity at galaxies scales. We consider an exact spherically symmetric solutionof $f(T)$ theory which is obtained from an approximate quadratic correction,and thus it is expected to hold for every realistic deviation from generalrelativity. Quantifying the deviation by a single parameter $Q$, and followingthe post-Newtonian approximation, we obtain the corresponding deviation in thegravitational potential, shear component, and effective surface density (ESD)profile. We used five stellar mass samples and divided them into blue and redto test the model dependence on galaxy color, and we modeled ESD profiles usingNavarro-Frenk-White (NFW) profiles. Based on the group catalog from the SloanDigital Sky Survey Data Release 7 (SDSS DR7) we finally extract$Q=2.138^{+0.952}_{-0.516}\times 10^{-5}\,$Mpc$^{-2}$ at $1\sigma$ confidence.This result indicates that $f(T)$ corrections on top of general relativity arefavored. Finally, we apply information criteria, such as the AIC and BIC ones,and although the dependence of $f(T)$ gravity on the off-center effect impliesthat its optimality needs to be carefully studied, our analysis shows that$f(T)$ gravity is more efficient in fitting the data comparing to generalrelativity and $\Lambda$CDM paradigm, and thus it offers a challenge to thelatter.

Galaxy-galaxy lensing data: $f(T)$ gravity challenges general relativity