We show the emergence of light localization in arrays of coupled optical waveguides with randomness only in the imaginary part of their refractive index and develop a one-parameter scaling theory for the normalized participation number of Floquet-Bloch modes. This localization introduces a different length scale in the decay of the autocorrelation function of a paraxial beam propagation. Our results are relevant to a vast family of systems with randomness in the dissipative part of their impedance spatial profile.