Rough volatility models have become a prominent tool in quantitative finance due to their ability to cap- ture the rough nature of financial time series. However, these models typically have a non-Markovian structure, and this poses significant computational challenges. Existing methods for approximating these models often involve either complex quadrature techniques or require optimization algorithms op- erating in high-dimensional spaces, making them difficult and computationally intensive to implement in practice. This work introduces a novel and highly efficient quadrature rule for a Markovian approx- imation of rough volatility models, along with its theoretical error bounds. We verify the error bounds through a detailed error analysis and conduct several experiments on option pricing, demonstrating that the proposed method outperforms other state-of-the-art methodologies in terms of efficiency and accuracy across a range of roughness parameters. A further advantage of the approach is its ease to implement it in practice.