The magnetic field affects the motion of electrons and the orientation of spins in solids, but it is believed to have little impact on the crystal structure. This common perception has been challenged recently by ferromagnetic shape-memory alloys, where the spin-lattice coupling is so strong that crystallographic axes even in a fixed sample are forced to rotate, following the direction of moments. One would, however, least expect any structural change to be induced in antiferromagnets where spins are antiparallel and give no net moment. Here we report on such unexpected magnetic shape-memory effects that take place ironically in one of the best-studied 2D antiferromagnets, La2-xSrxCuO4 (LSCO). We find that lightly-doped LSCO crystals tend to align their b axis along the magnetic field, and if the crystal orientation is fixed, this alignment occurs through the generation and motion of crystallographic twin boundaries. Both resistivity and magnetic susceptibility exhibit curious switching and memory effects induced by the crystal-axes rotation; moreover, clear kinks moving over the crystal surfaces allow one to watch the crystal rearrangement directly with a microscope or even bare eyes.