We report a two-dimensional tetragonal Titanium Carbide (TiC) monolayer sheet with distinguished structure and properties based on comprehensive first-principles calculations. The TiC sheet exhibits a novel zigzag-shaped buckling structure with all atoms being quasiplanar tetracoordinate, as favored by strong in-plane C2p-Ti3d bonding and synergetic out-of-plane electronic delocalization. This unique structure endows the sheet with high kinetic stability and anisotropic mechanical properties. Moreover, the TiC sheet displays orientation-dependent electronic properties derived from its special rectangular symmetry, with indirect band gap of ~0.2 eV and substantial ferromagnetism along its edges, thus promising for wide applications in nanoelectronics.