Transitions Fe − Fg = ΔF = ±2 between the excited and ground levels of the hyperfine structure of the Cs D2 atomic line in an external magnetic field of 300–3000 G have been studied for the first time with the use of σ+ and σ− circularly polarized radiation. Selection rules forbid these transitions in zero magnetic field. At the same time, the probabilities of these transitions in a magnetic field increase significantly; for this reason, we refer to these transitions as magnetically induced transitions. The following rule has been found for the intensities of 24 magnetically induced Fg = 3 → Fe = 5 and Fg = 4 → Fe = 2 transitions: the intensities of magnetically induced transitions with ΔF = +2 are maximal (the number of such magnetically induced transitions is also maximal) in the case of σ+ polarized radiation, whereas the intensities of magnetically induced transitions with ΔF = −2 are maximal (the number of such transitions is also maximal) in the case of σ− σ+ and σ− polarized radiation can reach several orders of magnitude; i.e., anomalous circular dichroism is observed. For an experimental test, absorption spectra of a Cs-filled nanocell with the thickness equal to half the wavelength of resonant laser radiation = 852 nm have been analyzed in order to separately detect magnetically induced transitions. The experiment is in good agreement with the theory. Possible applications have been discussed.