We present elliptic flow of strange and multi-strange hadrons ($K_{s}^{0}$, $\Lambda$, $\bar{\Lambda}$, $\phi$, $\Xi^{-}$, and $\overline{\Xi}^{+}$) at mid-rapidity in isobar collisions ($^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr) at $\sqrt{s_{\mathrm {NN}}}$ = 200 GeV. The transverse momentum ($p_{T}$) dependence of elliptic flow ($v_{2}$) is presented for minimum bias and various collision centrality intervals. We studied the number of constituent quark (NCQ) scaling of $v_{2}$ in these isobar collisions. Average elliptic flow ($\left\langle v_{2}\right\rangle$) has been observed to increase from central to peripheral collisions. The ratio of $\left\langle v_{2}\right\rangle$ between isobar species shows a deviation from unity that is consistent with the difference in nuclear structure and deformation in these species. A system size dependence of $v_{2}$ is also observed among isobar, Cu+Cu, Au+Au, and U+U systems.