Recently, Lee et al. [Nano Lett. 21, 4305 (2021)] synthesized the monochalcogenide GeSe in a polar phase, referred to as the $\ensuremath{\gamma}$-phase. Motivated by this work, we study the shift current of $\ensuremath{\gamma}$-GeSe and its tunability via an in-plane uniaxial strain. Using first-principles calculations, we uncover the electronic structure of strained $\ensuremath{\gamma}$-GeSe systems. We then calculate the frequency-dependent shift current conductivities at various strains. The tunability increases the shift current to $\ensuremath{\sim}40$ $\ensuremath{\mu}{\mathrm{A/V}}^{2}$ for visible light. Moreover, the direction of the shift current can be inverted by a light strain. Markedly, noticeable behavior is found in the zero-frequency limit, which can be indicative of band inversion and electronic phase transition driven by the strain. Our results suggest that the shift current can be tangible proof of bulk electronic states of $\ensuremath{\gamma}$-GeSe.