We investigated the electrodynamics of superconducting NbTi thin films using terahertz time-domain spectroscopy. In temperature-dependent measurements, the real part of the optical conductivity provides information on the superconducting gap and yields a critical temperature of 7 K, while the imaginary part is related to the superfluid density and the London penetration depth. We also examined pair-breaking effects under both in-plane and out-of-plane magnetic fields up to 7 T at 1.53 K. For in-plane magnetic fields, vortex contributions are negligible, and the field primarily acts as a pair-breaking perturbation. The superconducting properties under these conditions are analyzed using the Skalski-Betbeder-Matibet-Weiss theory. In contrast, when the magnetic field is applied perpendicular to the plane, vortices emerge in the mixed state and contribute additional low frequency spectral weight. By comparing the in-plane and out-of-plane responses, we identify the vortex induced contribution to the terahertz electrodynamics.