  The initial geometry effect on collective flows, which are inherited from
initial projectile structure, is studied in relativistic heavy-ion collisions
of $^{12}$C + Au by using a multi-phase transport model (AMPT). Elliptic flow
($v_2$) and triangular flow ($v_3$) which are significantly resulted from the
chain and triangle structure of $^{12}\mathrm{C}$ with three-$\alpha$ clusters,
respectively, in central $^{12}\mathrm{C}$+$^{197}\mathrm{Au}$ collisions are
compared with the flow from the Woods-Saxon distribution of nucleons in
$^{12}\mathrm{C}$. $v_3/v_2$ is proposed as a probe to distinguish the pattern
of $\alpha$-clustered $^{12}\mathrm{C}$. This study demonstrates that the
initial geometry of the collision zone inherited from nuclear structure can be
explored by collective flow at the final stage in heavy-ion collisions.
