The cross section of the process $e^+e^- rightarrow etaJ/psi$ is measured at center-of-mass energies from $sqrt{s} =$ 4.178 to 4.600 GeV using data samples corresponding to a total integrated luminosity of 11 fb$^{-1}$ collected with the BESIII detector operating at the BEPCII storage ring. The dependence of the cross section on $sqrt{s}$ shows an enhancement around $4.2$ GeV. While the shape of the cross section cannot be fully explained with a single $psi(4160)$ or $psi(4260)$ state, a coherent sum of the two states does provide a reasonable description of the data.