The sixth-generation (6G) wireless systems aim to achieve ultra-high data rates and enhanced connectivity, driven by the increasing demand for broadband services and interactive applications. However, achieving such high data rates introduces significant challenges, such as intersymbol interference (ISI), which degrades signal quality and system performance. This paper proposes a novel reconfigurable intelligent surface (RIS)-assisted single-carrier (SC) frequency domain equalization (FDE) to mitigate ISI and enhance broadband connectivity. The RIS reflection coefficients are configured to maximize the received signal power at the user equipment (UE) by compensating for the phase of the dominant-tap in the end-to-end channel of the proposed system. This configuration enables coherent signal combining at the receiver, thereby enhancing signal quality and overall system performance. The performance of the proposed system is analyzed over frequency-selective Rayleigh fading channels, and the pairwise error probability (PEP) expression and upper bound for the bit error rate (BER) are derived. Analytical and simulation results demonstrate that the proposed framework consistently outperforms the state-of-the-art cyclic prefix (CP) SC-RIS system, achieving up to two orders of magnitude improvement in terms of BER. Moreover, diversity analysis shows that while conventional CP transmission achieves a diversity order of 1, the proposed RIS-assisted framework attains a higher order equal tokλ, which corresponds to the shape parameter of the distribution of the weighted sum power of the end-to-end channel. This parameter scales linearly with both the number of RIS elements and the number of effective channel taps, thereby enabling enhanced diversity in the presence of richer multipath propagation and larger RIS arrays. Finally, performance analysis explicitly demonstrates that increasing the number of RIS elements and channel taps further improves system performance, highlighting the advantages of RIS-aided spatial configuration and multipath diversity exploitation.