Terahertz (THz) communication has been widely considered as a key enabler for future wireless systems. However, due to the strong directivity and severe attenuation of THz signals, the communication performance relies heavily on the existence of a line-of-sight (LoS) link. To deal with this problem, a reconfigurable intelligent surface (RIS) that modifies the wireless channel through intelligent signal reflection has gained much attention recently. In this paper, we propose an efficient near-field RIS-assisted wideband THz channel estimation scheme. Key idea of the proposed scheme, referred to as the polar-domain frequency-dependent RIS-assisted channel estimation (PF -RCE), is to exploit the polar-domain sparsity of the near-field channel and common support property of the wideband THz channel. To the best of our knowledge, this is the first work that investigates the characteristics of RIS-assisted wideband THz channel in the near- filed region and provides an efficient channel estimation scheme. From the numerical evaluations, we demonstrate that the proposed PF-RCE scheme achieves a significant performance gain over the conventional THz channel estimation schemes in terms of the normalized mean square error (NMSE).