The Langevin diffusion is reversible with respect to the density $\rho(x)=e^{-U(x)}$. This property is more transparent when the SDE is written as $$ dX_t = \nabla \log \rho(X_t) dt + \sqrt{2} dW_t $$ and is the basis of MCMC methods based on Langevin diffusions; see e.g.
Exponential convergence of Langevin diffusions and their discrete approximations
In fact, random-walk based MCMC methods (like random walk Metropolis) with target density $\rho(x)$, can be viewed as weak approximations to the corresponding Langevin diffusion; see e.g. Theorem 5.1 of
Metropolis integration schemes for self-adjoint diffusions
In particular, random walk Metropolis doesn’t even explicitly involve the gradient of $U$, but by virtue of being reversible, can weakly approximate the Langevin diffusion.