Incorporating for the first time both the spin and isospin degrees of freedom explicitly in transport model simulations of intermediate-energy heavy-ion collisions, we observe that a local spin polarization appears during collision process. Most interestingly, it is found that the nucleon spin up-down differential transverse flow is a sensitive probe of the spin-orbit interaction, providing a novel approach to probe both the density and isospin dependence of the in-medium spin-orbit coupling that is important for understanding the structure of rare isotopes and synthesis of superheavy elements. 24.10.Lx, 13.88.+e The spin-orbit coupling is common to the motion of many objects in nature from quarks, nucleons, and electrons to planets and stars. In nuclear physics, it has been very well known for a long time that the spin-orbit coupling is crucial for understanding the structure of finite nuclei, such as the magic numbers [1,2]. However, many interesting questions regarding the in-medium spin-orbit coupling, especially its density and isospin dependence, remain unresolved although in free space it has been well determined from nucleon-nucleon (NN) scattering data [3]. Indeed, several phenomena observed or predicted in studying properties of nuclear structures have been providing us some useful information about the inmedium spin-orbit interaction. For instance, the kink of the charge radii of lead isotopes can only be explained by introducing a weakly isospin-dependent spin-orbit coupling [4,5]. Moreover, strong experimental evidences of a decreasing spin-orbit coupling strength with increasing neutron excess were reported [6,7]. Furthermore, new experiments are currently being carried out at several laboratories to explore the density and isospin dependence of the spin-orbit coupling by comparing energy splittings of certain orbits in the so-called "bubble" nuclei [8,9] with those in normal nuclei [10]. The knowledge of the in-medium spin-orbit interaction is useful for understanding properties of drip-line nuclei [11], the astrophysical r-process [12], and the location of stability island for superheavy elements [13,14].While effects of the spin-orbit interaction on nuclear structure have been studied extensively, very little is known about its effects in heavy-ion collisions. Within the time-dependent Hartree-Fock (TDHF) calculations the nucleon spin-orbit interaction was found to affect the fusion threshold energy [15] and lead to a local spin polarization [16,17]. In non-central relativistic heavyion collisions at 200 GeV/nucleon the partonic spin-orbit coupling was found to lead to a global quark spin polarization [18]. However, to our best knowledge, no study on effects of the spin-orbit interaction in intermediateenergy heavy-ion collisions has been carried out yet. On the other hand, several facilities for spin-polarized beams have been developed for about twenty years. It has already been shown that spin-polarized projectile fragments in peripheral collisions are measurable through the angular distrib...