An effective range theory is used to study the elastic scattering of electrons by the ground state of hydrogen atoms in weakly coupled plasma environments for low electron energies. The plasma screening effect is represented by screened Coulomb potentials (SCPs) of Debye type. Highly correlated and variationally determined wavefunctions for H− in plasmas are used to determine the effective range of the ion states. The results for S-wave singlet phase shifts for the incident electron momentum in the range [0, 0.75] au are reported, to the best of our knowledge, for the first time in the literature. For the unscreened case, our reported results are in good agreement with some of the most accurate results available in the literature.