The ratio of branching fractions of $B_c^+ \to B_s^0 \pi^+$ and $B_c^+ \to J/\psi \pi^+$ decays is measured with proton-proton collision data of a centre-of-mass energy of $13\text{TeV}$. The data were collected with the LHCb experiment during 2016--2018, corresponding to an integrated luminosity of $5.4 \text{fb}^{-1}$. The $B_s^0$ mesons are reconstructed via the decays $B_s^0 \to J/\psi \phi$ and $B_s^0 \to D_s^- \pi^+$. The ratio of branching fractions is measured to be $\mathcal{B}(B_c^+ \to B_s^0 \pi^+)/\mathcal{B}(B_c^+ \to J/\psi \pi^+) = 91 \pm 10 \pm 8 \pm 3$ where the first uncertainty is statistical, the second is systematic and the third is due to the knowledge of the branching fractions of the intermediate state decays.