  We use simulated cluster member galaxies from Illustris TNG300-1 to develop a
technique for measuring the galaxy cluster mass accretion rate (MAR) that can
be applied directly to observations. We analyze 1318 IllustrisTNG clusters of
galaxies with $M_{200c}>10^{14}$M$_\odot$ and $0.01\leq z \leq 1.04$. The MAR
we derive is the ratio between the mass of a spherical shell located in the
infall region and the time for the infalling shell to accrete onto the
virialized region of the cluster. At fixed redshift, an $\sim 1$ order of
magnitude increase in $M_{200c}$ results in a comparable increase in MAR. At
fixed mass, the MAR increases by a factor of $\sim 5$ from $z=0.01$ to
$z=1.04$. The MAR estimates derived from the caustic technique are unbiased and
lie within 20% of the MARs based on the true mass profiles. This agreement is
crucial for observational derivation of the MAR. The IllustrisTNG results are
also consistent with (i) previous merger tree approaches based on N-body dark
matter only simulations and with (ii) previously determined MARs of real
clusters based on the caustic method. Future spectroscopic and photometric
surveys will provide MARs of enormous cluster samples with mass profiles
derived from both spectroscopy and weak lensing. Combined with future larger
volume hydrodynamical simulations that extend to higher redshift, the MAR
promises important insights into evolution of massive systems of galaxies.
