We describe the fabrication and characterization of magnesium diboride (MgB2) thin films for applications in superconducting devices. MgB2 shows great potential as a superconducting thin-film material due to its high transition temperature (Tc ≅ 39 K) and its level of nonlinear kinetic inductance that could enable a large current-controlled phase shift for accessibility to higher frequencies (0.5 – 3 THz). Compared to other high-temperature superconductors like YBa2Cu3O7 (YBCO), FeSe, and BaFe2As2 that require complex deposition techniques and have intricate crystal structures, MgB2 stands out due to its simple synthesis process and suitability for thin-film fabrication. We measure Coplanar Waveguide (CPW) and inverted microstrip MgB2 resonators that yield an internal quality factor of up to 15,000 at 4.2 K. By DC-biasing 3-μm wide CPW and inverted microstrip transmission lines, we demonstrate current-tunable phase-delays between 0 and 2π radians, showcasing the nonlinear kinetic inductance in MgB2. Understanding the total loss and nonlinear kinetic inductance of MgB2 allows for the design and realization of THz frequency superconducting devices, which are crucial for astrophysics and quantum sensors. MgB2 thin films find applications in Hot Electron Bolometers (HEBs), Thermal Kinetic Inductance Detectors (TKIDs), THz Traveling Wave Parametric Amplifiers (TWPAs), and THz frequency multipliers.