We construct the moduli cone stack $\backslash mathfracM\eta trop$ of tropical '{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on $\backslash mathfracM\eta trop$ and show that the tropical intersection theory agrees with the intersection theory on the moduli stack $\backslash mathfracM¯\eta$ of '{e}tale covers (i.e., coverings of twisted algebraic curves). We apply the tropical intersection theory on $\backslash mathfracM\eta trop$ to calculate the intersection numbers of Psi-classes on the moduli space $\backslash mathfracM¯g,n$ of $n$-marked genus $g$ curves. We also define the moduli stack $\backslash mathfracM\eta log$ of logarithmic '{e}tale covers and describe the tropicalization map from $\backslash mathfracM\eta log$ to the Artin fan of $\backslash mathfracM\eta trop$.