Stereodynamics of the collisional reaction between mutually aligned or oriented reactants has been a striking topic of chemical dynamics for decades. However, the stereodynamic aspects are scarcely revealed for the low-energy collision with a randomly oriented target. Here in the dissociative charge-exchange reaction between randomly oriented O2 and low-energy Ar+, we, using the three-dimensional ion velocity map imaging technique, clearly observe a linear alignment and a nearly isotropic distribution of the O+ yields along the collision axis. These observations are rationalized with the Doppler kinetic models in which the O2 bond is assumed to be parallel or unparallel to the collision axis of the large impact parameter collision. The linearly aligned O+, as the predominant yield, is produced in the parallel collision, while a rotating O2+, as the intermediate in the unparallel collision, leads to the isotropic distribution of O+.