The coupled cluster based linear response theory (CCLRT) with four-component relativistic spinors is employed to compute the electric field gradients (EFG) of Cl-35, Br-79, and I-127 nuclei. The EFGs resulting from these calculations are combined with experimental nuclear quadrupole coupling constants (NQCC) to determine the nuclear quadrupole moments (NQM), Q of the halide nuclei. Our estimated NQMs [Cl-35 = -81.12 mb,Br-79 = 307.98 mb, and I-127 = -688.22 mb] agree well with the new atomic values [Cl-35 = -81.1(1.2), Br-79 = 302(5), and I-127 = -680(10) mb] obtained via Fock space multireference coupled cluster method with the Dirac-Coulomb-Breit Hamiltonian. Although our estimated Q(Br-79) value deviates from the accepted reference value of 313(3) mb, it agrees well with the recently recommended value, Q(Br-79) = 308.7(20) mb. Good agreement with current reference data indicates the accuracy of the proposed value for these halogen nuclei and lends credence to the results obtained via CCLRT approach. The electron affinities yielded by this method with no extra cost are also in good agreement with experimental values, which bolster our belief that the NQMs values for halogen nuclei derived here are reliable.