A compact, cryocooler cooled Nb3Sn superconducting magnet system for a Cerenkov free electron laser has been designed, fabricated and tested. The magnet is positioned directly behind the electron gun of the laser system. The solenoidal field compresses and guides a tube-shaped 100 A, 500 kV electron beam. A two-stage GM cryocooler, equipped with a first generation ErNi5 regenerator, cools the epoxy impregnated solenoid down to the operating temperature of about 7.5 K. This leaves a conservative operational margin for the MJR type of Nb3Sn conductor of about 350% (I c) at 3T. Current leads with HTS sections between the first and second stage of the cryocooler effectively reduce the conductive heat leak. In the warm bore, 60 mm in diameter and 680 mm long, an operational magnetic field of 2 T has been achieved during laser operation without any quench. The field homogeneity is better than 99.5% over 450 mm axial length. Design details and test results of this magnet system are presented.