  Galaxy-galaxy lensing has emerged as a powerful probe of the dark matter
halos of galaxies, but is subject to contamination if intrinsically aligned
satellites of the lens galaxy are used as part of the source sample. We present
a measurement of this intrinsic shear using 200,747 lens galaxies from the
Sloan Digital Sky Survey (SDSS) spectroscopic sample and a sample of satellites
selected using photometric redshifts. The mean intrinsic shear at transverse
separations of 30--446$h^{-1}$ kpc is constrained to be
$-0.0062<\Delta\gamma<+0.0066$ (99.9 per cent confidence, including identified
systematics), which limits contamination of the galaxy-galaxy lensing signal to
at most $\sim 15$ per cent on these scales. We present these limits as a
function of transverse separation and lens luminosity. We furthermore
investigate shear calibration biases in the SDSS, which can also affect
galaxy-galaxy lensing, and conclude that the shear amplitude is calibrated to
better than 18 per cent. This includes noise-induced calibration biases in the
ellipticity, which are small for the sample considered here, but which can be
more important if low signal-to-noise or poorly resolved source galaxies are
used.
