Yes. It can be measured in spectra of the moon.
A paper The solar gravitational redshift from HARPS-LFC
Moon spectra describes the measurment of red-shifts in Iron absorption lines in the spectrum of the moon which result from gravitational redshift from the sun.
The difficulty in measuring these redshifts is not their scale (equivalent to motion of about ...
Gravitational waves should be redshifted.
The gravitational wave signal of an inspiralling binary system, which drifts across a range of frequencies, does not however yield the redshift of the binary system, since changing the redshift is indistinguishable from changing the mass of the system.
In practice, what is usually done is to estimate the redshift ...