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[en] In analogy to f(R) theory, recently a new modified gravity theory, namely the so-called f(T) theory, has been proposed to drive the current accelerated expansion without invoking dark energy. In the present work, by extending Bisabr's idea, we try to constrain f(T) theories with the varying fine structure 'constant', α≡e2/hc. We find that the constraints on f(T) theories from the observational Δα/α data are very severe. In fact, they make f(T) theories almost indistinguishable from ΛCDM model.