  We introduce a new method to construct closed rigid (unobstructed)
associative submanifolds in the twisted connected sum $G_2$-manifolds [Kov03,
KL11, CHNP15]. More precisely, we prove a gluing theorem of asymptotically
cylindrical (ACyl) associative submanifolds in ACyl $G_2$-manifolds under a
hypothesis that can be interpreted as a transverse Lagrangian intersection
condition. This is analogous to the gluing theorem for $G_2$-instantons
introduced in [SW15]. We rephrase the hypothesis in the special cases where the
ACyl associative submanifolds are obtained from holomorphic curves or special
Lagrangians in ACyl Calabi-Yau $3$-folds. In this way we find many new
associative submanifolds which are diffeomorphic to $S^3$, $\mathbf R\mathbf
P^3$ or $\mathbf R\mathbf P^3\#\mathbf R\mathbf P^3$. To lay the foundation for
the gluing theorem we also study the moduli space of ACyl associative
submanifolds with a natural topology. We prove that the moduli space is locally
homeomorphic to the zero set of a smooth map between two finite dimensional
spaces whose index depends only on the asymptotic cross section.
