  The study of R\'enyi mutual information (RMI) sheds light on the AdS/CFT
correspondence beyond classical order. In this article, we study the R\'enyi
mutual information between two intervals at large distance in two-dimensional
holographic warped conformal field theory, which is conjectured to be dual to
the gravity on AdS3 or warped AdS3 spacetime under the Dirichlet-Newman
boundary conditions. By using the operator product expansion of twist operators
up to level 3, we read the leading oder and the next-toleading order RMI in the
large central charge and small cross-ratio limits. The leading order result is
furthermore confirmed using the conformal block expansion. Finally, we match
the next-to-leading result by a 1-loop calculation in the bulk.
