We derive the analytical formula of the ratio of the ionization rates of degenerate valence π_± orbitals of prealigned linear molecules in strong circularly polarized (CP) laser fields. Interestingly, our theory shows that the ionization ratio for molecular orbitals with opposite azimuthal quantum numbers ± - m - (e.g., π_±) is identical to that for atomic orbitals with the same ± - m - (e.g., p±). In general, the electron counter-rotating to the CP laser field tunnels more easily, not only for atoms but also for linear molecules. Our theoretical predictions are then verified by numerically solving the three-dimensional time-dependent Schrödinger equation for the ionization of the prealigned nitric oxide (NO) molecule in strong CP laser fields. Due to the spin-orbital coupling in the electronic ground state of NO and the sensitivity of ionization to the sense of electron rotation, the ionization of NO in CP fields can produce spin-polarized photoelectrons with high controllability of spin polarization up to 100%.