To support intelligent vehicular services, vehicular ad-hoc networks (VANET) require high-speed communications from vehicles to infrastructure (V2I). To meet such demands, the Terahertz (THz) band, with abundant spectrum resources, is envisioned as a promising solution. However, a premise problem is channel modeling for THz V2I communications. In this paper, ray-tracing (RT) techniques are utilized to analyze the V2I channel in an urban scenario at 300 GHz. Channel statistics, including path loss, shadow fading, etc, are thoroughly characterized. The parameters of multi-path components (MPCs) and similarity of MPCs existing on identical streets are analyzed and modeled. Furthermore, the birth and death processes of MPCs are carefully characterized and modeled. A new criterion, namely, the virtual transmitter position scheme, is proposed to determine the birth and death of MPCs and the evolution of MPCs during their lifetime. Based on this, a ray-tracing assisted stochastic channel model (RTA-SCM), is proposed, which combines the RT technique and stochastic processes. The effectiveness and accuracy of RTA-SCM are validated by comparing it against RT data and geometry-based stochastic models. The proposed model can be utilized in time-varying THz V2I communications.