Semiconductor quantum dots (QDs) integrated with photonic nanowires are one of the representative platforms for high-purity single photonic sources. However, conventional photonic nanowires suffer from severe scattering at the edge owing to the small footprint. For this reason, tapered structures have been adopted to achieve directional emission with minimized scattering, and hence, high light collection efficiency. So far, various tapered structures have been demonstrated by using top-down etching fabrication or catalyst-assisted growth. However, these approaches can induce critical issues for QD integrated photonic devices such as an etching damage, an inclusion of multiple QDs in a wire, a misalignment of QD with respect to the wire axis center, or a contamination of QD by the catalyst. Therefore, developing a catalyst-free, site-controlled growth technique is essential for high-quality tapered nanowire structures. In this work, we propose a site-selectively grown photonic rocket structure, which consists of a pencil-like nanowire and a pyramid acting as a single-mode waveguide and a coupler, respectively. Since this structure is defined by stable crystal facets, the dimensions of the structure, especially its tapering angle, are determined precisely. Most significantly, a single QD can be formed at the apex, deterministically aligned to the axis center of the photonic structure. We analyzed the propagating mode inside the photonic nanowire and pyramid coupler using finite-difference time-domain simulations. This photonic rocket structure produces directional emission owing to the pyramid coupler, resulting in 2.9 (2.0) times larger light collection efficiency with a numerical aperture of 0.3 (0.7), compared to the nanowire structure alone.