Annealing between sticky ends of DNA is an intermediate step in ligation. It can also be utilized to program specific binding sites for DNA tile and origami assembly. This reaction is generally understood as a bimolecular reaction dictated by the local concentration of the sticky ends. Its dependence on the relative orientation between the sticky ends, however, is less understood. Here we report on the interactions between DNA sticky ends using the coarse-grained oxDNA model; specifically, we consider how the orientational alignment of the double-stranded DNA (dsDNA) segments affects the time required for the sticky ends to bind, τb. We specify the orientation of the dsDNA segments with three parameters: θ, which measures the angle between the helical axes, and ϕ1 and ϕ2, which measure rotations of each strand around the helical axis. We find that the binding time depends strongly on both θ and ϕ2: ∼20-fold change with θ and 10-fold change with ϕ2. The binding time is the fastest when the helical axes of duplexes are pointing toward each other and the sticky ends protrude from the farthest two points. Our result is relevant for predicting hybridization efficiency of sticky ends that are rotationally restricted.