In this paper, we study a new intelligent refracting surface (IRS)-assisted high-mobility communication with the IRS deployed in a high-speed moving vehicle to assist its passenger's communication with a static base station (BS) on the roadside. The vehicle's high Doppler frequency results in a fast fading channel between the BS and the passenger/user, which renders channel estimation for the IRS with a large number of refracting elements a more challenging task as compared to the conventional case with low-mobility users only. In order to mitigate the Doppler effect and reap the full IRS passive beamforming gain with low training overhead, we propose a new and efficient transmission protocol to execute channel estimation and IRS refraction design for data transmission. Specifically, by exploiting the quasi-static channel between the IRS and user both moving at the same high speed, we first estimate the cascaded BS-IRS-user channel with the Doppler effect compensated. Then, we estimate the instantaneous BS-user fast fading channel (without IRS refraction) and tune the IRS refraction over time accordingly to align the cascaded channel with the BS-user direct channel, thus maximizing the IRS's passive beamforming gain as well as converting their combined channel from fast to slow fading. Simulation results show the effectiveness of the proposed channel estimation scheme and passive beamforming design as compared to various benchmark schemes.