The US HEP Magnet Development Program is developing accelerator insert coils based on REBCO coated conductors. These insert coils will operate in high dipole or quadrupole background fields and enhance the field generated by the outsert coils made of Nb$_3$Sn or NbTi conductors. The inserts are of canted $\cos\theta$ (CCT) design configuration, which effectively intercepts the accumulation of azimuthal stress that can potentially damage the conductors. Through the collaboration with Advanced Conductor Technologies, we use the CORC® round wire due to its potential to offer high engineering current density in a mechanically and magnetically isotropic conductor form. The design and fabrication of the CORC® CCT dipole insert coils is presented. These coils were also tested at 77 K and 4.2 K in self-field, and we report on the coil performance including quench current and magnetic field measurements in the coil aperture.