There is nothing preventing a priest from adopting. Pfleger has two adoptive sons. Another Chicago priest, George Clement, also adopted one or two boys. Both did so with the full support of the Archdiocese of Chicago, after a little initial reluctance, and the approval of John Paul II.
If so, then it was changed. At the time he and Clement adopted it was against the rules and quite a big deal was made over it -- including wondering if they were going to force them to give the children up. And I would never expect Bernardin to follow the rules, so his support doesn't impress me.