We obtain the exact ground-state energy of the quasi-one-dimensional restricted ±J Ising spin glass in a uniform magnetic field using the transfer matrix method. Magnetic field dependence allows us to derive the magnetization as a function of concentration and magnetic field. It turns out that, in the limit of zero field, the magnetization tends to a nonzero value with a singular dependence on the magnetic field. We derive the explicit form of the singularity in thermodynamic quantities such as energy E≃E_{0}+m_{0}h+E_{1}e^{-h_{0}/h}, which is an essential singularity known as Griffiths singularity. We confirm our analytical results using the numerical approach based on iterative equations for energy.