  We show that for any integer $t \ge 2$, every properly edge colored
$n$-vertex graph with average degree at least $(\log n)^{2+o(1)}$ contains a
rainbow subdivision of a complete graph of size $t$. Note that this bound is
within $(\log n)^{1+o(1)}$ factor of the lower bound. This also implies a
result on the rainbow Tur\'{a}n number of cycles.
