  We demonstrate a general method to measure the quantum state of an angular
momentum of arbitrary magnitude. The (2F+1) x (2F+1) density matrix is
completely determined from a set of Stern-Gerlach measurements with (4F+1)
different orientations of the quantization axis. We implement the protocol for
laser cooled Cesium atoms in the 6S_{1/2}(F=4) hyperfine ground state and apply
it to a variety of test states prepared by optical pumping and Larmor
precession. A comparison of input and measured states shows typical
reconstruction fidelities of about 0.95.
