A PT-symmetric nonlocal Davey-Stewartson I equation is considered, in which $\bar u(x,y,t)$ in the classical equation is replaced by $\bar u(-x,-y,t)$. Using the nonlinear constraint from 2+1 dimensions to 1+1 dimensions and Darboux transformation in 1+1 dimensions, 2m x 2n dromion solutions are obtained. It is proved that under certain conditions, the derived solutions are always globally defined and decay exponentially at spacial infinity. Moreover, each asymptotic solution as t tends to infinity has exactly 4mn peaks. The local behavior of each peak is also given.