Superconducting magnets enable energy-frontier accelerators by generating strong magnetic fields to steer and focus the particles. Although high-temperature superconductors such as REBa$_2$Cu$_3$O$_x$ (REBCO RE = rare earth) hold a strong potential for generating a higher magnetic field than Nb-Ti and Nb$_3$Sn, the associated magnet and conductor technology for accelerator applications is still in its infancy. The U.S. Magnet Development Program is developing REBCO magnet technology in collaboration with industry. Here we report an experiment on making a dipole magnet called C3 using commercial high-temperature superconducting CORC® wires. The magnet, following a canted cosθ design, generated a dipole field of 5.99 T at 4.2 K in its clear aperture of 65 mm at 6.795 kA when a resistive voltage of 105 μV appeared across one of the coils in the magnet. The stored energy was 53 kJ at the peak field. The magnet showed no degradation in the current-carrying capability at 4.2 K after the thermal cycle. We report on the detailed design, fabrication, and performance of the C3 magnet that can be of interest to potential users of this emerging technology. We also discuss issues and research needs to inform future REBCO magnet development. The experiment represented another step to addressing if the high-temperature superconducting accelerator magnet technology can increase the discovery capability of future particle accelerators.