No one can apply to be pope of the catholic church.
(x) this is technically not true for some Anglican orders that later became Catholics? Maybe? (I never remember the rules of the ordinariate.) So maybe he could first become a priest in Anglican Church, then switch to Catholicism, then become a bishop, then a Cardinal, then a Pope? It's a long shot though.
edit: ahhh the married priests in Ordinariate cannot become bishops. So he would need to have first his marriage annulled I guess.