A design of a read out system for a superconducting gyroscope to be used in an orbiting Gyroscope Relativity Experiment is discussed. The "London Moment" of the superconducting rotor, which lies along the spin axis of the rotor, will be measured with a SQUID type magnetometer. The SQUID will be built around the gyro rotor, with a very close spacing to give an inductance between 10-8and 10-9Hy. A SQUID of this design should resolve 10-4φo. The angular resolution of the gyroscope will then be arc-second, which is sufficient for the intended experiment.