Recently, we presented a new approach for a compact radio-frequency (RF) accelerator structure and demonstrated the functionality of the individual components: acceleration units and focusing elements. In this paper, we combine these units to form a working accelerator structure including a matching section between the ion source extraction grids and the RF-acceleration unit. The matching section consist of six electrostatic quadrupoles (ESQs) fabricated using 3D-printing techniques. The matching section enables us to capture twice the amount of beam and match the beam envelope to conditions for an acceleration lattice. We present data from an integrated accelerator consisting of the source, matching section, and an ESQ doublet sandwiched between two RF-acceleration units.