  We study the percolation transition in growing networks under an Achlioptas
process (AP). At each time step, a node is added in the network and, with the
probability $\delta$, a link is formed between two nodes chosen by an AP. We
find that there occurs the percolation transition with varying $\delta$ and the
critical point $\delta_c=0.5149(1)$ is determined from the power-law behavior
of order parameter and the crossing of the fourth-order cumulant at the
critical point, also confirmed by the movement of the peak positions of the
second largest cluster size to the $\delta_c$. Using the finite-size scaling
analysis, we get $\beta/\bar{\nu}=0.20(1)$ and $1/\bar{\nu}=0.40(1)$, which
implies $\beta \approx 1/2$ and $\bar{\nu} \approx 5/2$. The Fisher exponent
$\tau = 2.24(1)$ for the cluster size distribution is obtained and shown to
satisfy the hyperscaling relation.
