This paper introduces a novel framework for rough volatility using rough differential equations (RDEs). The key innovation is a canonical joint lift of a Brownian motion and a low-regularity adapted stochastic rough path, such as fractional Brownian motion with Hurst parameter less than 1/2. This lift, defined via Itô integrals and shuffle relations, yields a geometric rough path that allows the price and volatility processes to be modeled as the solution to a single RDE. The framework offers significant flexibility: correlation between price and volatility can be introduced either through correlated drivers or directly in the dynamics, and path-dependent volatility models are naturally accommodated. The authors extend lead-lag approximations to the fractional setting, proving convergence rates for piecewise linear, hybrid, and mollifier approximations, which serve as numerical schemes. The paper validates the approach with numerical experiments and calibrates a simple new RDE-based rough volatility model to market data, demonstrating good fit. This work provides a versatile alternative to stochastic Volterra equations for rough volatility, leveraging the well-developed theory of rough paths and enabling efficient simulation and calibration.