The RF coupling coil (RFCC) module of MICE is where muons that have been cooled within the MICE absorber focus (AFC) modules are re-accelerated to their original longitudinal momentum. The RFCC module consists of four 201.25 MHz RF cavities in a 1.4 meter diameter vacuum vessel. The muons are kept within the RF cavities by the magnetic field generated by a superconducting coupling solenoid that goes around the RF cavities. The coupling solenoid will be cooled using a pair of 4 K pulse tube cooler that will generate 1.5 W of cooling at 4.2 K. The magnet will be powered using a 300 A two-quadrant power supply. This report describes the ICST engineering design of the coupling solenoid for MICE.