  We obtain the exact ground state energy of the quasi-one dimensional
restricted $\pm J$ 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 $E\simeq E_0+m_0
h + E_1e^{-h_0/h}$, which is an essential singularity known as Griffiths
singularity. We confirm our analytical results using the numerical approach
based on iterative equations for energy.
