  We use direct numerical simulations of decaying primordial hydromagnetic
turbulence with helicity to compute the resulting gravitational wave (GW)
production and its degree of circular polarization. We find a clear dependence
of the polarization of the resulting GWs on the fractional helicity of the
turbulent source and we show that driven magnetic fields produce GWs more
efficiently than magnetic fields that are initially present, leading to larger
spectral amplitudes. The helicity does not have a huge impact on the maximum
spectral amplitude in any of the two types of turbulence considered. However,
the GW spectrum at wave numbers away from the peak becomes smaller for larger
values of the magnetic fractional helicity. The degree of circular polarization
approaches zero at frequencies below the peak, and reaches its maximum at the
peak. At higher frequencies, it stays finite if the magnetic field is initially
present, and it approaches zero if it is driven. We predict that the spectral
peak of the GW signal can be detected by LISA if the turbulent energy density
is at least $\sim 3\%$ of the radiation energy density, and the characteristic
scale is a hundredth of the horizon at the electroweak scale. We show that the
resulting GW polarization is unlikely to be detectable by the anisotropies
induced by our proper motion in the dipole response function of LISA. Such
signals can, however, be detectable by cross-correlating data from the
LISA-Taiji network for turbulent energy densities of $\sim 5\%$, and fractional
helicity of 0.5 to 1. Second-generation space-based GW detectors, such as BBO
and DECIGO, would allow for the detection of a larger range of the GW spectrum
and smaller amplitudes of the magnetic field.
