This study describes the relativistic q-Gaussian laser beam's stimulated Raman scattering (SRS) in an unmagnetized plasma. Moreover, the influence of the pump laser's relativistic self-focusing on the SRS process has been investigated. Using variational theory, we derived analytical solutions to the coupled nonlinear wave equations describing the pump, EPW, and scattered waves. The resulting equations were numerically solved to see the impacts of laser and plasma characteristics on the dynamics of the pump beam and its influence on the power of scattered waves. The power of the scattered wave was observed to be significantly altered via the self-focusing action of the pump beam, where when the effect of self-focus increases, it leads to an increase in the effect of stimulated Raman scattering. The stimulated Raman scattering yield is investigated based on the laser beam's and plasma's intensity. The main finding is that as q increases, the SRS yield increases, and as the intensity of the laser beam and plasma density increase, the SRS yield also increases. The scattering of the self-focused beam takes place at a greater distance than the beam of the pump, due to the relatively diminished level of scattered power. The value of the integrated reflection increases with the increase of q and the growth rate.