  The spatial covariant gravities provide a natural way to including odd-order
spatial derivative terms into the gravitational action, which breaks the parity
symmetry at gravitational sector. A lot of parity-violating scalar-tensor
theories can be mapped to the spatial covariant framework by imposing the
unitary gauge. This provides us with a general framework for exploring the
parity-violating effects in primordial gravitational waves (PGWs). The main
purpose of this paper is to investigate the polarization of PGWs in the spatial
covariant gravities and their possible observational effects. To this end, we
first construct the approximate analytical solution to the mode function of the
PGWs during the slow-roll inflation by using the uniform asymptotic
approximation. With the approximate solution, we calculate explicitly the power
spectrum and the corresponding circular polarization of the PGWs analytically.
It is shown that the new contributions to power spectrum from spatial covariant
gravities contain two parts, one from the parity-preserving terms and the other
from the parity-violating terms. While the parity-preserving terms can only
affect the overall amplitudes of PGWs, the parity-violating terms induce
nonzero circular polarization of PGWs, i.e., the left-hand and right-hand
polarization modes of GWs have different amplitudes. The observational
implications of this nonzero circular polarization is also briefly discussed.
