We study a magnetic molecule that exhibits spin tunneling and is free to rotate about its anisotropy axis. Exact low-energy eigenstates of the molecule that are superpositions of spin and rotational states are obtained. We show that parameter α=2(ℏS)2/(IΔ) determines the ground state of the molecule. Here ℏS is the spin, I is the moment of inertia, and Δ is the tunnel splitting. The magnetic moment of the molecule is zero at α<αc=[1−1/(2S)2]−1 and non-zero at α>αc. At α→∞ the spin of the molecule localizes in one of the directions along the anisotropy axis.