  The NANOGrav collaboration has recently reported evidence for the existence
of a stochastic gravitational wave background in the 1-100 nHz frequency range.
We argue that such background could have been produced by magneto-hydrodynamic
(MHD) turbulence at the QCD scale. From the NANOGrav measurement one can infer
the magnetic field parameters: comoving field strength close to microGauss and
a correlation length close to 10\% of the Hubble radius at the QCD phase
transition epoch. We point out that the turbulent decay of a non-helical
magnetic field with such parameters leads to a magnetic field at the
recombination epoch, which would be sufficiently strong to provide a solution
to the Hubble tension problem, as recently proposed. We also show that the MHD
turbulence interpretation of the NANOGrav signal can be tested via measurements
of the relic magnetic field in the voids of the large scale structure, with
gamma-ray telescopes like CTA.
